**Chaotic Dynamics**

In common usage, "chaos" means "a state of disorder". However, in chaos theory, the term is defined more precisely. Although there is no universally accepted mathematical definition of chaos, a commonly used definition says that, for a dynamical system to be classified as chaotic, it must have the following properties:

- it must be sensitive to initial conditions;
- it must be topologically mixing; and
- its periodic orbits must be dense.

The requirement for sensitive dependence on initial conditions implies that there is a set of initial conditions of positive measure which do not converge to a cycle of any length.

Read more about this topic: Chaos Theory

### Other articles related to "chaotic, chaotic dynamics":

... A nonlinear dynamical system exhibits

**chaotic**hysteresis if it simultaneously exhibits

**chaotic dynamics**(chaos theory) and hysteresis ... If

**chaotic dynamics**appear either prior to or just after such jumps, or are persistent throughout each of the various equilibrium states, then the system is said to exhibit

**chaotic**hysteresis ...

**Chaotic dynamics**are irregular and bounded and subject to sensitive dependence on initial conditions ...

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