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Generating chaos via decentralized linear state feedback and a class of nonlinear functions

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  • Lu, Jun Guo

Abstract

This paper proposes a general chaotification algorithm for a class of nonlinear discrete-time dynamical systems. Based on a given nonlinear discrete-time system, the new chaotification algorithm uses the decentralized linear state feedback control and a class of nonlinear functions that are only required to satisfy some mild assumptions to construct a chaotic nonlinear system. The sine and sawtooth function used in the existing literature on chaotification only are the special cases of the proposed nonlinear function. Based on the corrected version of the Marotto theorem, we mathematically prove that the constructed nonlinear system is indeed chaotic in the sense of Li and Yorke. In particular, an explicit formula for the computation of chaotification parameters is also obtained. The theoretical results in this paper can be used to supervise one to construct different chaotification algorithms.

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  • Lu, Jun Guo, 2005. "Generating chaos via decentralized linear state feedback and a class of nonlinear functions," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 403-413.
    • Handle: RePEc:eee:chsofr:v:25:y:2005:i:2:p:403-413
    DOI: 10.1016/j.chaos.2004.11.039
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    Cited by:

    1. Wu, Xiaoqun & Lu, Jun-an & Iu, Herbert H.C. & Wong, Siu-Chung, 2007. "Suppression and generation of chaos for a three-dimensional autonomous system using parametric perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 811-819.
    2. Zhang, Ting & Wang, Jiang & Fei, Xiangyang & Deng, Bin, 2007. "Synchronization of coupled FitzHugh–Nagumo systems via MIMO feedback linearization control," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 194-202.
    3. Wang, Bo & Wen, Guangjun, 2009. "On the synchronization of uncertain master–slave chaotic systems with disturbance," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 145-151.

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