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Existence and uniqueness of limit cycle for a class of nonlinear discrete-time systems. (English) Zbl 1142.39307
Summary: 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.

39A11 Stability of difference equations (MSC2000)
92B05 General biology and biomathematics
Full Text: DOI
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