Asymptotic Stability Analysis Applied in Two and Three-Dimensional Discrete Systems to Control Chaos

Abstract

Asymptotic stability analysis applied to stabilize unstable fixed points and to control chaotic motions in two and three-dimensional discrete dynamical systems. A new set of parameter values obtained which stabilizes an unstable fixed point and control the chaotic evolution to regularity. The output of the considered model and that of the adjustable system continuously compared by a typical feedback and the difference used by the adaptation mechanism to modify the parameters. Suitable numerical simulation which are used thoroughly discussed and parameter values are adjusted. The findings are significant and interesting. This strategy has some advantages over many other chaos control methods in discrete systems but, however it can be applied within some limitations.

Keywords

• asymptotic stability
• control parameter
• chaos
• lyapunov exponents