Chaos Theory - Chaotic Dynamics

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:

  1. it must be sensitive to initial conditions;
  2. it must be topologically mixing; and
  3. 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":

Chaotic Hysteresis
... 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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