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48 relations: Absolute value, Autonomous system (mathematics), Characteristic polynomial, Complex number, Damping ratio, Derivative, Diffeomorphism, Differentiable manifold, Differential equation, Dynamical system, Eigenvalues and eigenvectors, Equilibrium point, Exponential decay, Exponential stability, Gromov–Hausdorff convergence, Hartman–Grobman theorem, Heat equation, Hurwitz polynomial, Hyperstability, Jacobian matrix and determinant, Linear approximation, Linear differential equation, Linear stability, Linearization, Lp space, Lyapunov function, Lyapunov stability, Mathematics, Matrix (mathematics), Maximum principle, Orbit (dynamics), Orbital stability, Oscillation, Pendulum, Periodic point, Phase space, Qualitative theory of differential equations, Real number, Routh–Hurwitz stability criterion, Routh–Hurwitz theorem, Smoothness, Square matrix, Stability criterion, Stability radius, Structural stability, Vector field, Von Neumann stability analysis, Wolfram Demonstrations Project.
Absolute value
In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.
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Autonomous system (mathematics)
In mathematics, an autonomous system or autonomous differential equation is a system of ordinary differential equations which does not explicitly depend on the independent variable.
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Characteristic polynomial
In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots.
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Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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Damping ratio
Damping is an influence within or upon an oscillatory system that has the effect of reducing, restricting or preventing its oscillations.
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Derivative
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
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Diffeomorphism
In mathematics, a diffeomorphism is an isomorphism of smooth manifolds.
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Differentiable manifold
In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.
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Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives.
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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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Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
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Equilibrium point
In mathematics, specifically in differential equations, an equilibrium point is a constant solution to a differential equation.
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Exponential decay
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.
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Exponential stability
In control theory, a continuous linear time-invariant system (LTI) is exponentially stable if and only if the system has eigenvalues (i.e., the poles of input-to-output systems) with strictly negative real parts.
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Gromov–Hausdorff convergence
In mathematics, Gromov–Hausdorff convergence, named after Mikhail Gromov and Felix Hausdorff, is a notion for convergence of metric spaces which is a generalization of Hausdorff convergence.
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Hartman–Grobman theorem
In mathematics, in the study of dynamical systems, the Hartman–Grobman theorem or linearization theorem is a theorem about the local behavior of dynamical systems in the neighbourhood of a hyperbolic equilibrium point.
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Heat equation
The heat equation is a parabolic partial differential equation that describes the distribution of heat (or variation in temperature) in a given region over time.
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Hurwitz polynomial
In mathematics, a Hurwitz polynomial, named after Adolf Hurwitz, is a polynomial whose roots (zeros) are located in the left half-plane of the complex plane or on the imaginary axis, that is, the real part of every root is zero or negative.
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Hyperstability
In stability theory, hyperstability is a property of a system that requires the state vector to remain bounded if the inputs are restricted to belonging to a subset of the set of all possible inputs.
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Jacobian matrix and determinant
In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.
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Linear approximation
In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function).
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Linear differential equation
In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where,..., and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of an unknown function of the variable.
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Linear stability
In mathematics, in the theory of differential equations and dynamical systems, a particular stationary or quasistationary solution to a nonlinear system is called linearly unstable if the linearization of the equation at this solution has the form \frac.
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Linearization
In mathematics, linearization is finding the linear approximation to a function at a given point.
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Lp space
In mathematics, the Lp spaces are function spaces defined using a natural generalization of the ''p''-norm for finite-dimensional vector spaces.
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Lyapunov function
In the theory of ordinary differential equations (ODEs), Lyapunov functions are scalar functions that may be used to prove the stability of an equilibrium of an ODE.
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Lyapunov stability
Various types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems.
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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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Matrix (mathematics)
In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
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Maximum principle
In mathematics, the maximum principle is a property of solutions to certain partial differential equations, of the elliptic and parabolic types.
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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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Orbital stability
In mathematical physics and the theory of partial differential equations, the solitary wave solution of the form u(x,t).
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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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Pendulum
A pendulum is a weight suspended from a pivot so that it can swing freely.
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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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Qualitative theory of differential equations
In mathematics, the qualitative theory of differential equations studies the behavior of differential equations by means other than finding their solutions.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Routh–Hurwitz stability criterion
In control system theory, the Routh–Hurwitz stability criterion is a mathematical test that is a necessary and sufficient condition for the stability of a linear time invariant (LTI) control system.
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Routh–Hurwitz theorem
In mathematics, the Routh–Hurwitz theorem gives a test to determine whether all roots of a given polynomial lie in the left half-plane.
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Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
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Square matrix
In mathematics, a square matrix is a matrix with the same number of rows and columns.
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Stability criterion
In control theory, and especially stability theory, a stability criterion establishes when a system is stable.
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Stability radius
The stability radius of an object (system, function, matrix, parameter) at a given nominal point is the radius of the largest ball, centered at the nominal point, all of whose elements satisfy pre-determined stability conditions.
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Structural stability
In mathematics, structural stability is a fundamental property of a dynamical system which means that the qualitative behavior of the trajectories is unaffected by small perturbations (to be exact ''C''1-small perturbations).
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Vector field
In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space.
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Von Neumann stability analysis
In numerical analysis, von Neumann stability analysis (also known as Fourier stability analysis) is a procedure used to check the stability of finite difference schemes as applied to linear partial differential equations.
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Wolfram Demonstrations Project
The Wolfram Demonstrations Project is an organized, open-source collection of small (or medium-size) interactive programs called Demonstrations, which are meant to visually and interactively represent ideas from a range of fields.
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Diverge (stability theory), Stability (mathematics), Stability theorem.
References
[1] https://en.wikipedia.org/wiki/Stability_theory
