Dynamical system and Mathematical and theoretical biology

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Difference between Dynamical system and Mathematical and theoretical biology

Dynamical system vs. Mathematical and theoretical biology

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space. Mathematical and theoretical biology is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories.

Bifurcation diagram

In mathematics, particularly in dynamical systems, a bifurcation diagram shows the values visited or approached asymptotically (fixed points, periodic orbits, or chaotic attractors) of a system as a function of a bifurcation parameter in the system.

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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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Chaos theory

Chaos theory is a branch of mathematics focusing on the behavior of dynamical systems that are highly sensitive to initial conditions.

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Computer

A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming.

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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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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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Mathematical model

A mathematical model is a description of a system using mathematical concepts and language.

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Ordinary differential equation

In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives.

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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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Partial differential equation

In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.

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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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Recurrence relation

In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms.

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Stochastic process

--> In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a collection of random variables.

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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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