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Existence and uniqueness of limit cycle for a class of nonlinear discrete-time systems

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  • Sun, Yeong-Jeu

Abstract

In this paper, the definition of the exponentially stable limit cycle for nonlinear discrete-time systems is firstly introduced. The limit cycle phenomenon for a class of nonlinear discrete-time systems is investigated. Using analytic method, the existence and uniqueness of limit cycle for such systems can be guaranteed. Besides, the exponentially stable limit cycles, the period of oscillation, and guaranteed convergence rate can be correctly estimated. Finally, a numerical example is provided to illustrate the use of the main result.

Suggested Citation

  • Sun, Yeong-Jeu, 2008. "Existence and uniqueness of limit cycle for a class of nonlinear discrete-time systems," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 89-96.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:1:p:89-96
    DOI: 10.1016/j.chaos.2006.10.031
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    References listed on IDEAS

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    1. Cheng, Zunshui & Lin, Yiping & Cao, Jinde, 2006. "Dynamical behaviors of a partial-dependent predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 67-75.
    2. Ramos, J.I., 2006. "Piecewise-linearized methods for oscillators with limit cycles," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1229-1238.
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    Cited by:

    1. Sabatini, M., 2010. "Existence and uniqueness of limit cycles in a class of second order ODE’s with inseparable mixed terms," Chaos, Solitons & Fractals, Elsevier, vol. 43(1), pages 25-30.
    2. Sun, Yeong-Jeu, 2009. "Existence of self-oscillation for a class of nonlinear discrete-time systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 731-734.

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