The Case of Continuous-Time Systems

e-mail: zeraoulia@mail.univ-tebessa.dz, zelhadj12@yahoo.fr, sprott@physics.wisc.edu

Received December 9, 2011

We present a new method to generate
chaotic hyperbolic systems. The method is based on the knowledge
of a chaotic hyperbolic system and the use of a synchronization
technique. This procedure is called hyperbolification of
dynamical systems. The aim of this process is to create or
enhance the hyperbolicity of a dynamical system. In other
words, hyperbolification of dynamical systems produces chaotic
hyperbolic (structurally stable) behaviors in a system that
would not otherwise be hyperbolic. The method of
hyperbolification can be outlined as follows. We consider a
known ndimensional hyperbolic chaotic system as a drive system
and another ndimensional system as the response system plus a
feedback control function to be determined in accordance with a
specific synchronization criterion. We then consider the error
system and

apply a synchronization method, and find sufficient conditions for the errors to converge to zero and hence the synchronization between the two systems to be established. This means that we construct a 2*n*-dimensional continuoustime system that
displays a robust hyperbolic chaotic attractor. An illustrative
example is given to show the effectiveness of the proposed
hyperbolification method.

apply a synchronization method, and find sufficient conditions for the errors to converge to zero and hence the synchronization between the two systems to be established. This means that we construct a 2

Ref: E. Zeraoulia and J. C. Sprott, Journal of Experimental
and Theoretical Physics 115,
356-360 (2012)

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