The simplest chaotic dynamical system
is the Bernoulli shift described by Palmore :
Recently, chaotic dynamical systems become very popular in science and engineering.
Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley, Redwood City, Calif, USA, 1st edition, 1989.
of Tebessa, Algeria) has selected papers from the past decade pertaining to the topic announced in the title--both experimental and theoretical aspects of problems arising in the study of both discrete and continuous time chaotic dynamical systems
In practice, discrete-time chaotic dynamical systems
are more important than continuous ones, and many models including neural networks, biological process, physical process, and chemical process are described by discrete-time chaotic dynamical models .
Pecora and Carroll  introduced the idea of synchronization for possibly chaotic dynamical systems
. The synchronization phenomena are concerned with two identical systems, which can be coupled in such a way that the solution of one always converges to the solution of the other, independently of the initial conditions and parameters.
When the state vector and the output are perturbed due to some reason, a class of chaotic dynamical systems
can be described in the following equations:
In chaotic dynamical systems
theory, the largest Lyapunov exponent can be portrayed as a whole (long-term) average forecast error growth rate, which generally describes the divergence of nonlinear chaotic systems.
Rossetto, "Differential geometry and mechanics: applications to chaotic dynamical systems
," International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol.