Dynamical system


Dynamical System
EXPLORE THIS TOPIC IN the MathWorld Classroom

A means of describing how one state develops into another state over the course of time. Technically, a dynamical system is a smooth action of the reals or the integers on another object (usually a manifold). When the reals are acting, the system is called a continuous dynamical system, and when the integers are acting, the system is called a discrete dynamical system. If f is any continuous function, then the evolution of a variable x can be given by the formula

This equation can also be viewed as a difference equation

so defining


which can be read “as n changes by 1 unit, x changes by g(x).” This is the discrete analog of the differential equation


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