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Mathematical model of the time dependence of a point in space

This article is about the general aspects of dynamical systems. For the study field, see Dynamical systems theory.

"Dynamical" redirects here. For other uses, see Dynamical (disambiguation).

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured.^{[citation needed]} Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory

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