Chaotification via arbitrarily small feedback controls : Theory, method, and applications

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Original languageEnglish
Pages (from-to)549-570
Journal / PublicationInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number3
Publication statusPublished - Mar 2000
Externally publishedYes


In this paper, the problem of making a stable nonlinear autonomous system chaotic or enhancing the existing chaos of an originally chaotic system by using a small-amplitude feedback controller is studied. The designed controller is a linear feedback controller composed with a nonlinear modulo or sawtooth function, which can lead to uniformly bounded state vectors of the controlled system with positive Lyapunov exponents, thereby yielding chaotic dynamics. We mathematically prove that the controlled system is indeed chaotic in the sense of Li and Yorke. A few potential applications of the new chaotification algorithm are briefly discussed.