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262 relations: Abelian sandpile model, Aftershock, Albert J. Libchaber, Aleksandr Lyapunov, Algorithmic trading, American Association for the Advancement of Science, American Mathematical Monthly, American Mathematical Society, Amplitude death, Andrey Kolmogorov, Anosov diffeomorphism, Anthropology, Arnold's cat map, Astrophysics, Attractor, Étienne Ghys, BEAM robotics, Benoit Mandelbrot, Bernardo Huberman, Bifurcation theory, Biology, Bouncing ball, Brosl Hasslacher, Butterfly effect, Canada lynx, Cantor set, Cardiac cycle, Cardiotocography, Catastrophe theory, Causality, Celestial mechanics, Chao Tang, Chaos machine, Chaos theory in organizational development, Chaos: Making a New Science, Chaotic mixing, Chaotic scattering, Christiaan Huygens, Chua's circuit, Clifford A. Pickover, Cliodynamics, Complex adaptive system, Complex system, Complexity, Computational neuroscience, Computer science, Condition number, Confusion and diffusion, Continuous function, Contour advection, ..., Control of chaos, Coupled map lattice, Cryptographic primitive, Cryptography, David Malone (independent filmmaker), David Ruelle, Dense set, Determinism, Deterministic system, Dietmar Saupe, Differential equation, Dimension, Dimension (vector space), Discrete mathematics, DNA computing, Double pendulum, Duffing equation, Dye, Dynamical billiards, Dynamical system, Earthquake, Ecology, Economic bubble, Economics, Econophysics, Edge of chaos, Edward Norton Lorenz, Electrical engineering, Emergence, Engineering, Environmental science, Epidemic, Era (geology), Ergodic theory, Ergodicity, Evolution, Exponential growth, Feedback, Finance, Financial market, Florence, Floris Takens, Fractal, Fractal dimension, Functional analysis, Geology, George David Birkhoff, George Zaslavsky, Goldstone boson, Group development, Gutenberg–Richter law, Hadamard's dynamical system, Hénon map, Heinz-Otto Peitgen, Henri Poincaré, Horseshoe map, How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension, Hydrology, Ian Stewart (mathematician), Ilya Prigogine, Infinitesimal, Information theory, Initial condition, Interval (mathematics), Intrauterine hypoxia, Isabelle Stengers, Italy, Iteration, Ivar Ekeland, Ivars Peterson, J. Doyne Farmer, Jacques Hadamard, James A. Yorke, James Gleick, Jean-Pierre Eckmann, Jerk (physics), John Briggs (author), John Edensor Littlewood, Josephson effect, Julia set, Koch snowflake, Kolmogorov automorphism, Kolmogorov–Arnold–Moser theorem, Kuramoto model, Kurt Wiesenfeld, Landslide, Leon Glass, Leon O. Chua, LGP-30, Limit cycle, Linear system, List of chaotic maps, List of Jurassic Park characters, Logistic map, Lorenz system, Lyapunov exponent, Lyapunov time, Mandelbrot set, Martin Gutzwiller, Mary Cartwright, Mathematical model, Mathematics, Measure (mathematics), Menger sponge, Meteorology, Michael Berry (physicist), Michel Hénon, Microbiology, Millennium Bridge, London, Mitchell Feigenbaum, Mixing (mathematics), Moons of Pluto, National Institute of Mental Health, Neuron, New York Academy of Sciences, Niles Eldredge, Non-Euclidean geometry, Nonlinear system, Nonlinearity (journal), Normal distribution, Norman Packard, Office of Naval Research, Oleksandr Mykolayovych Sharkovsky, Open set, Operational amplifier, Orbit (dynamics), Oscillation, Otto Rössler, Paradigm shift, Parameter, Particle swarm optimization, Passive dynamics, Patterns in nature, Per Bak, Periodic point, Phase space, Philosophy, Physical Review Letters, Physics, Physics Letters, Physiology, Pierre Hohenberg, Plane (geometry), Poincaré map, Poincaré–Bendixson theorem, Politics, Polymer, Population dynamics, Population model, Position (vector), Predictability, Predictive modelling, Predrag Cvitanović, Princeton University Press, Proceedings of the USSR Academy of Sciences, Providence, Rhode Island, Pseudorandom noise, Psychology, Punctuated equilibrium, Quantum chaos, Quantum mechanics, Ralph Abraham (mathematician), Randomness, Rayleigh–Bénard convection, Rössler attractor, Recurrence plot, Robert L. Devaney, Robert May, Baron May of Oxford, Robert Shaw (physicist), Royal McBee, Santa Fe Institute, Scale invariance, Schizophrenia, Scientific American, Self-assembly, Self-organization, Self-organized criticality, Self-similarity, Sharkovskii's theorem, Sierpinski triangle, Social system, Sociology, Solar flare, Standard map, State-space representation, Stephen Jay Gould, Stephen Smale, Steven Strogatz, Swinging Atwood's machine, Symmetric-key algorithm, Synchronization of chaos, Team building, The Fractal Geometry of Nature, The Structure of Scientific Revolutions, Thomas Kuhn, Three-body problem, Tilt-A-Whirl, Topology, Traffic, Trajectory, Turbulence, Unintended consequences, Universality (dynamical systems), Van der Pol oscillator, War, Water cycle, Weather and climate, Well-posed problem, Wiktionary, Wildfire, Wilfred Bion, Wolf Prize in Physics. Expand index (212 more) »
Abelian sandpile model
The Abelian sandpile model, also known as the Bak–Tang–Wiesenfeld model, was the first discovered example of a dynamical system displaying self-organized criticality.
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Aftershock
An aftershock is a smaller earthquake that occurs after a previous large earthquake, in the same area of the main shock.
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Albert J. Libchaber
Albert Joseph Libchaber (born 23 October 1934, Paris) is a Detlev W. Bronk Professor at Rockefeller University.
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Aleksandr Lyapunov
Aleksandr Mikhailovich Lyapunov (Алекса́ндр Миха́йлович Ляпуно́в,; – November 3, 1918) was a Russian mathematician, mechanician and physicist.
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Algorithmic trading
Algorithmic trading is a method of executing a large order (too large to fill all at once) using automated pre-programmed trading instructions accounting for variables such as time, price, and volume to send small slices of the order (child orders) out to the market over time.
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American Association for the Advancement of Science
The American Association for the Advancement of Science (AAAS) is an American international non-profit organization with the stated goals of promoting cooperation among scientists, defending scientific freedom, encouraging scientific responsibility, and supporting scientific education and science outreach for the betterment of all humanity.
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American Mathematical Monthly
The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.
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American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
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Amplitude death
In the theory of dynamical systems, amplitude death is complete cessation of oscillations.
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Andrey Kolmogorov
Andrey Nikolaevich Kolmogorov (a, 25 April 1903 – 20 October 1987) was a 20th-century Soviet mathematician who made significant contributions to the mathematics of probability theory, topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity.
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Anosov diffeomorphism
In mathematics, more particularly in the fields of dynamical systems and geometric topology, an Anosov map on a manifold M is a certain type of mapping, from M to itself, with rather clearly marked local directions of "expansion" and "contraction".
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Anthropology
Anthropology is the study of humans and human behaviour and societies in the past and present.
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Arnold's cat map
In mathematics, Arnold's cat map is a chaotic map from the torus into itself, named after Vladimir Arnold, who demonstrated its effects in the 1960s using an image of a cat, hence the name.
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Astrophysics
Astrophysics is the branch of astronomy that employs the principles of physics and chemistry "to ascertain the nature of the astronomical objects, rather than their positions or motions in space".
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Attractor
In the mathematical field of dynamical systems, an attractor is a set of numerical values toward which a system tends to evolve, for a wide variety of starting conditions of the system.
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Étienne Ghys
Étienne Ghys (born 29 December 1954) is a French mathematician.
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BEAM robotics
BEAM robotics (from '''B'''iology, '''E'''lectronics, '''A'''esthetics and '''M'''echanics) is a style of robotics that primarily uses simple analogue circuits, such as comparators, instead of a microprocessor in order to produce an unusually simple design.
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Benoit Mandelbrot
Benoit B.  Mandelbrot  (20 November 1924 – 14 October 2010) was a Polish-born, French and American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life".
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Bernardo Huberman
Bernardo Huberman is a Fellow and vice president of the Core Innovation Team at.
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Bifurcation theory
Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations.
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Biology
Biology is the natural science that studies life and living organisms, including their physical structure, chemical composition, function, development and evolution.
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Bouncing ball
The physics of a bouncing ball concerns the physical behaviour of bouncing balls, particularly its motion before, during, and after impact against the surface of another body.
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Brosl Hasslacher
Brosl Hasslacher (May 13, 1941 – November 11, 2005) was a theoretical physicist.
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Butterfly effect
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.
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Canada lynx
The Canada lynx (Lynx canadensis) or Canadian lynx is a North American mammal of the cat family, Felidae.
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Cantor set
In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties.
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Cardiac cycle
The cardiac cycle is the performance of the human heart from the beginning of one heartbeat to the beginning of the next.
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Cardiotocography
Cardiotocography (CTG) is a technical means of recording the fetal heartbeat and the uterine contractions during pregnancy.
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Catastrophe theory
In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry.
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Causality
Causality (also referred to as causation, or cause and effect) is what connects one process (the cause) with another process or state (the effect), where the first is partly responsible for the second, and the second is partly dependent on the first.
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Celestial mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of celestial objects.
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Chao Tang
Chao Tang (汤超) is a Chair Professor of Physics and Systems Biology at Peking University.
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Chaos machine
In mathematics, a chaos machine is a class of algorithms constructed on the base of chaos theory (mainly deterministic chaos) to produce pseudo-random oracle.
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Chaos theory in organizational development
In organizational development, chaos theory is a subset of more general chaos theory that incorporates principles of quantum mechanics and presents them in a complex systems environment.
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Chaos: Making a New Science
Chaos: Making a New Science is a debut non-fiction book by James Gleick that initially introduced the principles and early development of the chaos theory to the public.
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Chaotic mixing
In chaos theory and fluid dynamics, chaotic mixing is a process by which flow tracers develop into complex fractals under the action of a fluid flow.
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Chaotic scattering
Chaotic scattering is a branch of chaos theory dealing with scattering systems displaying a strong sensitivity to initial conditions.
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Christiaan Huygens
Christiaan Huygens (Hugenius; 14 April 1629 – 8 July 1695) was a Dutch physicist, mathematician, astronomer and inventor, who is widely regarded as one of the greatest scientists of all time and a major figure in the scientific revolution.
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Chua's circuit
Chua's circuit (also known as a Chua circuit) is a simple electronic circuit that exhibits classic chaotic behavior.
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Clifford A. Pickover
Clifford Alan Pickover (born August 15, 1957) is an American author, editor, and columnist in the fields of science, mathematics, science fiction, innovation, and creativity and is employed at the IBM Thomas J. Watson Research Center in Yorktown, New York.
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Cliodynamics
Cliodynamics is a transdisciplinary area of research integrating cultural evolution, economic history/cliometrics, macrosociology, the mathematical modeling of historical processes during the longue durée, and the construction and analysis of historical databases.
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Complex adaptive system
A complex adaptive system is a system in which a perfect understanding of the individual parts does not automatically convey a perfect understanding of the whole system's behavior.
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Complex system
A complex system is a system composed of many components which may interact with each other.
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Complexity
Complexity characterises the behaviour of a system or model whose components interact in multiple ways and follow local rules, meaning there is no reasonable higher instruction to define the various possible interactions.
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Computational neuroscience
Computational neuroscience (also known as theoretical neuroscience or mathematical neuroscience) is a branch of neuroscience which employs mathematical models, theoretical analysis and abstractions of the brain to understand the principles that govern the development, structure, physiology and cognitive abilities of the nervous system.
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Computer science
Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.
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Condition number
In the field of numerical analysis, the condition number of a function with respect to an argument measures how much the output value of the function can change for a small change in the input argument.
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Confusion and diffusion
In cryptography, confusion and diffusion are two properties of the operation of a secure cipher identified by Claude Shannon in his 1945 classified report A Mathematical Theory of Cryptography. These properties, when present, work to thwart the application of statistics and other methods of cryptanalysis.
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Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
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Contour advection
Contour advection is a Lagrangian method of simulating the evolution of one or more contours or isolines of a tracer as it is stirred by a moving fluid.
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Control of chaos
In lab experiments that study chaos theory, approaches designed to control chaos are based on certain observed system behaviors.
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Coupled map lattice
A coupled map lattice (CML) is a dynamical system that models the behavior of non-linear systems (especially partial differential equations).
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Cryptographic primitive
Cryptographic primitives are well-established, low-level cryptographic algorithms that are frequently used to build cryptographic protocols for computer security systems.
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Cryptography
Cryptography or cryptology (from κρυπτός|translit.
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David Malone (independent filmmaker)
David Hugh Malone (born March 1962) is a British independent filmmaker, Green Party politician, and author of The Debt Generation.
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David Ruelle
David Pierre Ruelle (born 20 August 1935) is a Belgian-French mathematical physicist.
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Dense set
In topology and related areas of mathematics, a subset A of a topological space X is called dense (in X) if every point x in X either belongs to A or is a limit point of A, that is the closure of A is constituting the whole set X. Informally, for every point in X, the point is either in A or arbitrarily "close" to a member of A — for instance, every real number either is a rational number or has a rational number arbitrarily close to it (see Diophantine approximation).
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Determinism
Determinism is the philosophical theory that all events, including moral choices, are completely determined by previously existing causes.
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Deterministic system
In mathematics, computer science and physics, a deterministic system is a system in which no randomness is involved in the development of future states of the system.
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Dietmar Saupe
Dietmar Saupe (born 1954) is a fractal researcher and professor of computer science, Department of Computer and Information Science, University of Konstanz, Germany.
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Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives.
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Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
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Dimension (vector space)
In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field.
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Discrete mathematics
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.
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DNA computing
DNA computing is a branch of computing which uses DNA, biochemistry, and molecular biology hardware, instead of the traditional silicon-based computer technologies.
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Double pendulum
In physics and mathematics, in the area of dynamical systems, a double pendulum is a pendulum with another pendulum attached to its end, and is a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions.
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Duffing equation
The Duffing equation (or Duffing oscillator), named after Georg Duffing (1861–1944), is a non-linear second-order differential equation used to model certain damped and driven oscillators.
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Dye
A dye is a colored substance that has an affinity to the substrate to which it is being applied.
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Dynamical billiards
A billiard is a dynamical system in which a particle alternates between motion in a straight line and specular reflections from a boundary.
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Dynamical system
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space.
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Earthquake
An earthquake (also known as a quake, tremor or temblor) is the shaking of the surface of the Earth, resulting from the sudden release of energy in the Earth's lithosphere that creates seismic waves.
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Ecology
Ecology (from οἶκος, "house", or "environment"; -λογία, "study of") is the branch of biology which studies the interactions among organisms and their environment.
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Economic bubble
An economic bubble or asset bubble (sometimes also referred to as a speculative bubble, a market bubble, a price bubble, a financial bubble, a speculative mania, or a balloon) is trade in an asset at a price or price range that strongly exceeds the asset's intrinsic value.
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Economics
Economics is the social science that studies the production, distribution, and consumption of goods and services.
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Econophysics
Econophysics is an interdisciplinary research field, applying theories and methods originally developed by physicists in order to solve problems in economics, usually those including uncertainty or stochastic processes and nonlinear dynamics.
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Edge of chaos
The term edge of chaos is used to denote a transition space between order and disorder that is hypothesized to exist within a wide variety of systems.
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Edward Norton Lorenz
Edward Norton Lorenz (May 23, 1917 – April 16, 2008) was an American mathematician, meteorologist, and a pioneer of chaos theory.
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Electrical engineering
Electrical engineering is a professional engineering discipline that generally deals with the study and application of electricity, electronics, and electromagnetism.
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Emergence
In philosophy, systems theory, science, and art, emergence occurs when "the whole is greater than the sum of the parts," meaning the whole has properties its parts do not have.
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Engineering
Engineering is the creative application of science, mathematical methods, and empirical evidence to the innovation, design, construction, operation and maintenance of structures, machines, materials, devices, systems, processes, and organizations.
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Environmental science
Environmental science is an interdisciplinary academic field that integrates physical, biological and information sciences (including ecology, biology, physics, chemistry, plant science, zoology, mineralogy, oceanology, limnology, soil science, geology and physical geography (geodesy), and atmospheric science) to the study of the environment, and the solution of environmental problems.
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Epidemic
An epidemic (from Greek ἐπί epi "upon or above" and δῆμος demos "people") is the rapid spread of infectious disease to a large number of people in a given population within a short period of time, usually two weeks or less.
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Era (geology)
A geologic era is a subdivision of geologic time that divides an eon into smaller units of time.
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Ergodic theory
Ergodic theory (Greek: έργον ergon "work", όδος hodos "way") is a branch of mathematics that studies dynamical systems with an invariant measure and related problems.
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Ergodicity
In probability theory, an ergodic dynamical system is one that, broadly speaking, has the same behavior averaged over time as averaged over the space of all the system's states in its phase space.
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Evolution
Evolution is change in the heritable characteristics of biological populations over successive generations.
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Exponential growth
Exponential growth is exhibited when the rate of change—the change per instant or unit of time—of the value of a mathematical function is proportional to the function's current value, resulting in its value at any time being an exponential function of time, i.e., a function in which the time value is the exponent.
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Feedback
Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause-and-effect that forms a circuit or loop.
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Finance
Finance is a field that is concerned with the allocation (investment) of assets and liabilities (known as elements of the balance statement) over space and time, often under conditions of risk or uncertainty.
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Financial market
A financial market is a market in which people trade financial securities and derivatives such as futures and options at low transaction costs.
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Florence
Florence (Firenze) is the capital city of the Italian region of Tuscany.
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Floris Takens
Floris Takens (November 12, 1940 – June 20, 2010) was a Dutch mathematician known for contributions to the theory of chaotic dynamical systems.
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Fractal
In mathematics, a fractal is an abstract object used to describe and simulate naturally occurring objects.
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Fractal dimension
In mathematics, more specifically in fractal geometry, a fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the scale at which it is measured.
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Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense.
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Geology
Geology (from the Ancient Greek γῆ, gē, i.e. "earth" and -λoγία, -logia, i.e. "study of, discourse") is an earth science concerned with the solid Earth, the rocks of which it is composed, and the processes by which they change over time.
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George David Birkhoff
George David Birkhoff (March 21, 1884 – November 12, 1944) was an American mathematician best known for what is now called the ergodic theorem.
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George Zaslavsky
George M. Zaslavsky (Cyrillic: Георгий Моисеевич Заславский) (31 May 1935 – 25 November 2008) was a Soviet mathematical physicist and one of the founders of the physics of dynamical chaos.
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Goldstone boson
In particle and condensed matter physics, Goldstone bosons or Nambu–Goldstone bosons (NGBs) are bosons that appear necessarily in models exhibiting spontaneous breakdown of continuous symmetries.
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Group development
The goal of most research on group development is to learn why and how small groups change over time.
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Gutenberg–Richter law
In seismology, the Gutenberg–Richter law (GR law) expresses the relationship between the magnitude and total number of earthquakes in any given region and time period of at least that magnitude.
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Hadamard's dynamical system
In physics and mathematics, the Hadamard dynamical system (also called Hadamard's billiard or the Hadamard-Gutzwiller model) is a chaotic dynamical system, a type of dynamical billiards.
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Hénon map
The Hénon map is a discrete-time dynamical system.
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Heinz-Otto Peitgen
Heinz-Otto Peitgen (born April 30, 1945 in Bruch, Nümbrecht near Cologne) is a German mathematician and was President of Jacobs University from January 1, 2013 to December 31, 2013.
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Henri Poincaré
Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.
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Horseshoe map
In the mathematics of chaos theory, a horseshoe map is any member of a class of chaotic maps of the square into itself.
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How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension
"How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension" is a paper by mathematician Benoît Mandelbrot, first published in ''Science'' in 1967.
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Hydrology
Hydrology is the scientific study of the movement, distribution, and quality of water on Earth and other planets, including the water cycle, water resources and environmental watershed sustainability.
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Ian Stewart (mathematician)
Ian Nicholas Stewart (born 24 September 1945) is a British mathematician and a popular-science and science-fiction writer.
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Ilya Prigogine
Viscount Ilya Romanovich Prigogine (Илья́ Рома́нович Приго́жин; 28 May 2003) was a physical chemist and Nobel laureate noted for his work on dissipative structures, complex systems, and irreversibility.
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Infinitesimal
In mathematics, infinitesimals are things so small that there is no way to measure them.
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Information theory
Information theory studies the quantification, storage, and communication of information.
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Initial condition
In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted t.
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Interval (mathematics)
In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.
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Intrauterine hypoxia
Intrauterine hypoxia occurs when the fetus is deprived of an adequate supply of oxygen.
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Isabelle Stengers
Isabelle Stengers (born 1949) is a Belgian philosopher, noted for her work in the philosophy of science.
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Italy
Italy (Italia), officially the Italian Republic (Repubblica Italiana), is a sovereign state in Europe.
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Iteration
Iteration is the act of repeating a process, to generate a (possibly unbounded) sequence of outcomes, with the aim of approaching a desired goal, target or result.
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Ivar Ekeland
Ivar I. Ekeland (born 2 July 1944, Paris) is a French mathematician of Norwegian descent.
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Ivars Peterson
Ivars Peterson (born 4 December 1948) is an award-winning mathematics writer.
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J. Doyne Farmer
J.
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Jacques Hadamard
Jacques Salomon Hadamard ForMemRS (8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex function theory, differential geometry and partial differential equations.
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James A. Yorke
James A. Yorke (born August 3, 1941) is a Distinguished University Research Professor of Mathematics and Physics and former chair of the Mathematics Department at the University of Maryland, College Park.
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James Gleick
James Gleick (born August 1, 1954) is an American author and historian of science whose work has chronicled the cultural impact of modern technology.
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Jean-Pierre Eckmann
Jean-Pierre Eckmann (born 27 January 1944) is a mathematical physicist in the department of theoretical physics at the University of Geneva and a pioneer of chaos theory and social network analysis.
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Jerk (physics)
In physics, jerk is the rate of change of acceleration; that is, the time derivative of acceleration, and as such the second derivative of velocity, or the third time derivative of position.
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John Briggs (author)
John Briggs FRSGS (born 1945) is an American author and co-author of general audience nonfiction books in the fields of holistic physics; aesthetics in the arts; creativity, creative process, and consciousness studies.
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John Edensor Littlewood
John Edensor Littlewood FRS LLD (9 June 1885 – 6 September 1977) was an English mathematician.
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Josephson effect
The Josephson effect is the phenomenon of supercurrent—i.e. a current that flows indefinitely long without any voltage applied—across a device known as a Josephson junction (JJ), which consists of two superconductors coupled by a weak link.
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Julia set
In the context of complex dynamics, a topic of mathematics, the Julia set and the Fatou set are two complementary sets (Julia 'laces' and Fatou 'dusts') defined from a function.
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Koch snowflake
The Koch snowflake (also known as the Koch curve, Koch star, or Koch island) is a mathematical curve and one of the earliest fractal curves to have been described.
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Kolmogorov automorphism
In mathematics, a Kolmogorov automorphism, K-automorphism, K-shift or K-system is an invertible, measure-preserving automorphism defined on a standard probability space that obeys Kolmogorov's zero–one law.
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Kolmogorov–Arnold–Moser theorem
The Kolmogorov–Arnold–Moser theorem (KAM theorem) is a result in dynamical systems about the persistence of quasiperiodic motions under small perturbations.
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Kuramoto model
The Kuramoto model (or Kuramoto-Daido model), first proposed by Yoshiki Kuramoto (蔵本 由紀 Kuramoto Yoshiki), is a mathematical model used to describe synchronization.
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Kurt Wiesenfeld
Kurt Wiesenfeld is an American physicist working primarily on non-linear dynamics.
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Landslide
The term landslide or, less frequently, landslip, refers to several forms of mass wasting that include a wide range of ground movements, such as rockfalls, deep-seated slope failures, mudflows and debris flows.
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Leon Glass
Leon Glass (born 1943) is an American scientist who has studied various aspects of the application of mathematical and physical methods to biology, with special interest in vision, cardiac arrhythmia, and genetic networks.
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Leon O. Chua
Leon Ong Chua (born June 28, 1936) is an American electrical engineer and computer scientist.
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LGP-30
The LGP-30, standing for Librascope General Purpose and then Librascope General Precision, was an early off-the-shelf computer.
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Limit cycle
In mathematics, in the study of dynamical systems with two-dimensional phase space, a limit cycle is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity or as time approaches negative infinity.
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Linear system
A linear system is a mathematical model of a system based on the use of a linear operator.
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List of chaotic maps
In mathematics, a chaotic map is a map (.
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List of Jurassic Park characters
The following is a list of fictional characters from Michael Crichton's novel Jurassic Park, its sequel The Lost World, and their film adaptations, Jurassic Park and The Lost World: Jurassic Park.
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Logistic map
The logistic map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often cited as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations.
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Lorenz system
The Lorenz system is a system of ordinary differential equations first studied by Edward Lorenz.
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Lyapunov exponent
In mathematics the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close trajectories.
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Lyapunov time
In mathematics, the Lyapunov time is the characteristic timescale on which a dynamical system is chaotic.
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Mandelbrot set
The Mandelbrot set is the set of complex numbers c for which the function f_c(z).
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Martin Gutzwiller
Martin Charles Gutzwiller (12 October 1925 – 3 March 2014) was a Swiss-American physicist, known for his work on field theory, quantum chaos, and complex systems.
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Mary Cartwright
Dame Mary Lucy Cartwright, (17 December 1900 – 3 April 1998) was a British mathematician.
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Mathematical model
A mathematical model is a description of a system using mathematical concepts and language.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Measure (mathematics)
In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.
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Menger sponge
In mathematics, the Menger sponge (also known as the Menger cube, Menger universal curve, Sierpinski cube, or Sierpinski sponge) is a fractal curve.
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Meteorology
Meteorology is a branch of the atmospheric sciences which includes atmospheric chemistry and atmospheric physics, with a major focus on weather forecasting.
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Michael Berry (physicist)
Sir Michael Victor Berry, (born 14 March 1941), is a mathematical physicist at the University of Bristol, England.
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Michel Hénon
Michel Hénon (1931 in Paris – 7 April 2013 in Nice) was a French mathematician and astronomer.
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Microbiology
Microbiology (from Greek μῑκρος, mīkros, "small"; βίος, bios, "life"; and -λογία, -logia) is the study of microorganisms, those being unicellular (single cell), multicellular (cell colony), or acellular (lacking cells).
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Millennium Bridge, London
The Millennium Bridge, officially known as the London Millennium Footbridge, is a steel suspension bridge for pedestrians crossing the River Thames in London, England, linking Bankside with the City of London.
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Mitchell Feigenbaum
Mitchell Jay Feigenbaum (born December 19, 1944) is a mathematical physicist whose pioneering studies in chaos theory led to the discovery of the Feigenbaum constants.
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Mixing (mathematics)
In mathematics, mixing is an abstract concept originating from physics: the attempt to describe the irreversible thermodynamic process of mixing in the everyday world: mixing paint, mixing drinks, etc.
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Moons of Pluto
The dwarf planet Pluto has five moons down to a detection limit of about 1 km in diameter.
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National Institute of Mental Health
The National Institute of Mental Health (NIMH) is one of 27 institutes and centers that make up the National Institutes of Health (NIH).
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Neuron
A neuron, also known as a neurone (British spelling) and nerve cell, is an electrically excitable cell that receives, processes, and transmits information through electrical and chemical signals.
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New York Academy of Sciences
The New York Academy of Sciences (originally the Lyceum of Natural History) was founded in January 1817.
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Niles Eldredge
Niles Eldredge (born August 25, 1943) is a U.S. biologist and paleontologist, who, along with Stephen Jay Gould, proposed the theory of punctuated equilibrium in 1972.
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Non-Euclidean geometry
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry.
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Nonlinear system
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input.
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Nonlinearity (journal)
Nonlinearity is a peer-reviewed scientific journal published by IOP Publishing and the London Mathematical Society.
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Normal distribution
In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.
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Norman Packard
Norman Harry Packard (born 1954 in Billings, Montana) is a chaos theory physicist and one of the founders of the Prediction Company and ProtoLife.
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Office of Naval Research
The Office of Naval Research (ONR) is an organization within the United States Department of the Navy that coordinates, executes, and promotes the science and technology programs of the U.S. Navy and Marine Corps through schools, universities, government laboratories, nonprofit organizations, and for-profit organizations.
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Oleksandr Mykolayovych Sharkovsky
Oleksandr Mykolayovych Sharkovsky (also Sharkovskii) (Олекса́ндр Миколайович Шарко́вський) (born December 7, 1936) is a prominent Ukrainian mathematician most famous for developing Sharkovsky's theorem on the periods of discrete dynamical systems in 1964.
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Open set
In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.
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Operational amplifier
An operational amplifier (often op-amp or opamp) is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output.
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Orbit (dynamics)
In mathematics, in the study of dynamical systems, an orbit is a collection of points related by the evolution function of the dynamical system.
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Oscillation
Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states.
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Otto Rössler
Otto Eberhard Rössler (born 20 May 1940) is a German biochemist known for his work on chaos theory and the theoretical equation known as the Rössler attractor.
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Paradigm shift
A paradigm shift (also radical theory change), a concept identified by the American physicist and philosopher Thomas Kuhn (1922–1996), is a fundamental change in the basic concepts and experimental practices of a scientific discipline.
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Parameter
A parameter (from the Ancient Greek παρά, para: "beside", "subsidiary"; and μέτρον, metron: "measure"), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc.
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Particle swarm optimization
In computer science, particle swarm optimization (PSO) is a computational method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality.
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Passive dynamics
Passive dynamics refers to the dynamical behavior of actuators, robots, or organisms when not drawing energy from a supply (e.g., batteries, fuel, ATP).
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Patterns in nature
Patterns in nature are visible regularities of form found in the natural world.
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Per Bak
Per Bak (December 8, 1948 – October 16, 2002) was a Danish theoretical physicist who coauthored the 1987 academic paper that coined the term "self-organized criticality.".
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Periodic point
In mathematics, in the study of iterated functions and dynamical systems, a periodic point of a function is a point which the system returns to after a certain number of function iterations or a certain amount of time.
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Phase space
In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space.
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Philosophy
Philosophy (from Greek φιλοσοφία, philosophia, literally "love of wisdom") is the study of general and fundamental problems concerning matters such as existence, knowledge, values, reason, mind, and language.
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Physical Review Letters
Physical Review Letters (PRL), established in 1958, is a peer-reviewed, scientific journal that is published 52 times per year by the American Physical Society.
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Physics
Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
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Physics Letters
Physics Letters was a scientific journal published from 1962 to 1966, when it split in two series now published by Elsevier.
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Physiology
Physiology is the scientific study of normal mechanisms, and their interactions, which work within a living system.
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Pierre Hohenberg
Pierre C. Hohenberg (3 October 1934 – 15 December 2017) was a French-American theoretical physicist, who worked primarily on statistical mechanics.
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Plane (geometry)
In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.
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Poincaré map
In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower-dimensional subspace, called the Poincaré section, transversal to the flow of the system.
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Poincaré–Bendixson theorem
In mathematics, the Poincaré–Bendixson theorem is a statement about the long-term behaviour of orbits of continuous dynamical systems on the plane, cylinder, or two-sphere.
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Politics
Politics (from Politiká, meaning "affairs of the cities") is the process of making decisions that apply to members of a group.
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Polymer
A polymer (Greek poly-, "many" + -mer, "part") is a large molecule, or macromolecule, composed of many repeated subunits.
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Population dynamics
Population dynamics is the branch of life sciences that studies the size and age composition of populations as dynamical systems, and the biological and environmental processes driving them (such as birth and death rates, and by immigration and emigration).
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Population model
A population model is a type of mathematical model that is applied to the study of population dynamics.
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Position (vector)
In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point P in space in relation to an arbitrary reference origin O. Usually denoted x, r, or s, it corresponds to the straight-line from O to P. The term "position vector" is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus.
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Predictability
Predictability is the degree to which a correct prediction or forecast of a system's state can be made either qualitatively or quantitatively.
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Predictive modelling
Predictive modelling uses statistics to predict outcomes.
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Predrag Cvitanović
Predrag Cvitanović (born April 1, 1946) is a theoretical physicist regarded for his work in nonlinear dynamics, particularly his contributions to periodic orbit theory.
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Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University.
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Proceedings of the USSR Academy of Sciences
The Proceedings of the USSR Academy of Sciences (Доклады Академии Наук СССР, Doklady Akademii Nauk SSSR (DAN SSSR), Comptes Rendus de l'Académie des Sciences de l'URSS) was a Soviet journal that was dedicated to publishing original, academic research papers in physics, mathematics, chemistry, geology, and biology.
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Providence, Rhode Island
Providence is the capital and most populous city of the U.S. state of Rhode Island and is one of the oldest cities in the United States.
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Pseudorandom noise
In cryptography, pseudorandom noise (PRN) is a signal similar to noise which satisfies one or more of the standard tests for statistical randomness.
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Psychology
Psychology is the science of behavior and mind, including conscious and unconscious phenomena, as well as feeling and thought.
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Punctuated equilibrium
Punctuated equilibrium (also called punctuated equilibria) is a theory in evolutionary biology which proposes that once species appear in the fossil record the population will become stable, showing little evolutionary change for most of its geological history.
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Quantum chaos
Quantum chaos is a branch of physics which studies how chaotic classical dynamical systems can be described in terms of quantum theory.
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Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
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Ralph Abraham (mathematician)
Ralph H. Abraham (born July 4, 1936) is an American mathematician.
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Randomness
Randomness is the lack of pattern or predictability in events.
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Rayleigh–Bénard convection
Rayleigh–Bénard convection is a type of natural convection, occurring in a plane horizontal layer of fluid heated from below, in which the fluid develops a regular pattern of convection cells known as Bénard cells.
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Rössler attractor
The Rössler attractor is the attractor for the Rössler system, a system of three non-linear ordinary differential equations originally studied by Otto Rössler.
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Recurrence plot
In descriptive statistics and chaos theory, a recurrence plot (RP) is a plot showing, for a given moment in time, the times at which a phase space trajectory visits roughly the same area in the phase space.
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Robert L. Devaney
Robert Luke Devaney (born 1948) is an American mathematician, the Feld Family Professor of Teaching Excellence at Boston University.
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Robert May, Baron May of Oxford
Robert McCredie May, Baron May of Oxford, HonFAIB (born 8 January 1936) is an Australian scientist who has been Chief Scientific Adviser to the UK Government, President of the Royal Society, and a Professor at the University of Sydney and Princeton University.
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Robert Shaw (physicist)
Robert Stetson Shaw (born 1946) is an American physicist who was part of Eudaemonic Enterprises in Santa Cruz in the late 1970s and early 1980s.
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Royal McBee
Royal McBee was the computer manufacturing and retail division of Royal Typewriter which sold and serviced early computers RPC-4000 and RPC-9000.
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Santa Fe Institute
The Santa Fe Institute (SFI) is an independent, nonprofit theoretical research institute located in Santa Fe (New Mexico, United States) and dedicated to the multidisciplinary study of the fundamental principles of complex adaptive systems, including physical, computational, biological, and social systems.
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Scale invariance
In physics, mathematics, statistics, and economics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, thus represent a universality.
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Schizophrenia
Schizophrenia is a mental disorder characterized by abnormal social behavior and failure to understand reality.
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Scientific American
Scientific American (informally abbreviated SciAm) is an American popular science magazine.
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Self-assembly
Self-assembly is a process in which a disordered system of pre-existing components forms an organized structure or pattern as a consequence of specific, local interactions among the components themselves, without external direction.
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Self-organization
Self-organization, also called (in the social sciences) spontaneous order, is a process where some form of overall order arises from local interactions between parts of an initially disordered system.
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Self-organized criticality
In physics, self-organized criticality (SOC) is a property of dynamical systems that have a critical point as an attractor.
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Self-similarity
In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e. the whole has the same shape as one or more of the parts).
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Sharkovskii's theorem
In mathematics, Sharkovskii's theorem, named after Oleksandr Mykolaiovych Sharkovskii who published it in 1964, is a result about discrete dynamical systems.
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Sierpinski triangle
The Sierpinski triangle (also with the original orthography Sierpiński), also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal and attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles.
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Social system
In sociology, a social system is the patterned network of relationships constituting a coherent whole that exist between individuals, groups, and institutions.
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Sociology
Sociology is the scientific study of society, patterns of social relationships, social interaction, and culture.
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Solar flare
A solar flare is a sudden flash of increased Sun's brightness, usually observed near its surface.
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Standard map
The standard map (also known as the Chirikov–Taylor map or as the Chirikov standard map) is an area-preserving chaotic map from a square with side 2\pi onto itself.
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State-space representation
In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations or difference equations.
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Stephen Jay Gould
Stephen Jay Gould (September 10, 1941 – May 20, 2002) was an American paleontologist, evolutionary biologist, and historian of science.
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Stephen Smale
Stephen Smale (born July 15, 1930) is an American mathematician from Flint, Michigan.
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Steven Strogatz
Steven Henry Strogatz (born August 13, 1959) is an American mathematician and the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University.
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Swinging Atwood's machine
The swinging Atwood's machine (SAM) is a mechanism that resembles a simple Atwood's machine except that one of the masses is allowed to swing in a two-dimensional plane, producing a dynamical system that is chaotic for some system parameters and initial conditions.
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Symmetric-key algorithm
Symmetric-key algorithms are algorithms for cryptography that use the same cryptographic keys for both encryption of plaintext and decryption of ciphertext.
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Synchronization of chaos
Synchronization of chaos is a phenomenon that may occur when two, or more, dissipative chaotic systems are coupled.
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Team building
Team building is a collective term for various types of activities used to enhance social relations and define roles within teams, often involving collaborative tasks.
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The Fractal Geometry of Nature
The Fractal Geometry of Nature is a 1982 book by the Franco-American mathematician Benoît Mandelbrot.
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The Structure of Scientific Revolutions
The Structure of Scientific Revolutions (1962; second edition 1970; third edition 1996; fourth edition 2012) is a book about the history of science by the philosopher Thomas S. Kuhn.
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Thomas Kuhn
Thomas Samuel Kuhn (July 18, 1922 – June 17, 1996) was an American physicist, historian and philosopher of science whose controversial 1962 book The Structure of Scientific Revolutions was influential in both academic and popular circles, introducing the term paradigm shift, which has since become an English-language idiom.
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Three-body problem
In physics and classical mechanics, the three-body problem is the problem of taking an initial set of data that specifies the positions, masses, and velocities of three bodies for some particular point in time and then determining the motions of the three bodies, in accordance with Newton's laws of motion and of universal gravitation, which are the laws of classical mechanics.
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Tilt-A-Whirl
Tilt-A-Whirl is a flat ride similar to the Waltzer in Europe, designed for commercial use at amusement parks, fairs, and carnivals, in which it is commonly found.
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Topology
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.
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Traffic
Traffic on roads consists of road users including pedestrians, ridden or herded animals, vehicles, streetcars, buses and other conveyances, either singly or together, while using the public way for purposes of travel.
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Trajectory
A trajectory or flight path is the path that a massive object in motion follows through space as a function of time.
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Turbulence
In fluid dynamics, turbulence or turbulent flow is any pattern of fluid motion characterized by chaotic changes in pressure and flow velocity.
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Unintended consequences
In the social sciences, unintended consequences (sometimes unanticipated consequences or unforeseen consequences) are outcomes that are not the ones foreseen and intended by a purposeful action.
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Universality (dynamical systems)
In statistical mechanics, universality is the observation that there are properties for a large class of systems that are independent of the dynamical details of the system.
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Van der Pol oscillator
In dynamics, the Van der Pol oscillator is a non-conservative oscillator with non-linear damping.
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War
War is a state of armed conflict between states, societies and informal groups, such as insurgents and militias.
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Water cycle
The water cycle, also known as the hydrological cycle or the hydrologic cycle, describes the continuous movement of water on, above and below the surface of the Earth.
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Weather and climate
There is often confusion between weather and climate.
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Well-posed problem
The mathematical term well-posed problem stems from a definition given by Jacques Hadamard.
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Wiktionary
Wiktionary is a multilingual, web-based project to create a free content dictionary of all words in all languages.
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Wildfire
A wildfire or wildland fire is a fire in an area of combustible vegetation that occurs in the countryside or rural area.
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Wilfred Bion
Wilfred Ruprecht Bion DSO (8 September 1897 – 8 November 1979) was an influential British psychoanalyst, who became president of the British Psychoanalytical Society from 1962 to 1965.
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Wolf Prize in Physics
The Wolf Prize in Physics is awarded once a year by the Wolf Foundation in Israel.
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Applications of chaos theory, Chaology, Chaos (Mathematics), Chaos (mathematics), Chaos (physics), Chaos Theory, Chaotic behavior, Chaotic behavior in systems, Chaotic dynamical system, Chaotic dynamical systems, Chaotic map, Chaotic motion, Chaotic orbit, Chaotic system, Chaotic systems, Classical chaos, Deterministic chaos, Deterministic chaotic system, Disorganized, Nonchaotic behavior of quadratic differential systems, The order of choas.
References
[1] https://en.wikipedia.org/wiki/Chaos_theory
