Chaotifying continuous-time nonlinear autonomous systems

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Original languageEnglish
Article number1250232
Journal / PublicationInternational Journal of Bifurcation and Chaos
Volume22
Issue number9
Publication statusPublished - Sept 2012

Abstract

Based on the principle of chaotification for continuous-time autonomous systems, which relies on two basic properties of chaos, i.e. being globally bounded with necessary positive-zero-negative Lyapunov exponents, this paper derives a feasible and unified chaotification method for designing a general chaotic continuous-time autonomous nonlinear system. For a system consisting of a linear and a nonlinear subsystems, chaotification is achieved using separation of state variables, which decomposes the system into two open-loop subsystems interacting through mutual feedback resulting in an overall closed-loop nonlinear feedback system. Under the condition that the nonlinear feedback control output is uniformly bounded where the nonlinear function is of bounded-input/bounded-output, it is proved that the resulting system is chaotic in the sense of being globally bounded with a required placement of Lyapunov exponents. Several numerical examples are given to verify the effectiveness of the theoretical design. Since linear systems are special cases of nonlinear systems, the new method is also applicable to linear systems in general. © 2012 World Scientific Publishing Company.

Research Area(s)

  • Chaos, Chaotification, Continuous-time system, Global boundedness, Lyapunov exponent