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Existence and uniqueness of limit cycles in a class of second order ODE’s with inseparable mixed terms

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  • Sabatini, M.

Abstract

We prove a uniqueness result for limit cycles of the second order ODE x¨+x˙ϕ(x,x˙)+g(x)=0. Under mild additional conditions, we show that such a limit cycle attracts every non-constant solution. As a special case, we prove limit cycle’s uniqueness for an ODE studied in [5] as a model of pedestrians’ walk. This paper is an extension to equations with a non-linear g(x) of the results presented in [8].

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  • 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.
    • Handle: RePEc:eee:chsofr:v:43:y:2010:i:1:p:25-30
    DOI: 10.1016/j.chaos.2010.07.002
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    1. 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.
    2. Yu, P. & Han, M., 2007. "On limit cycles of the Liénard equation with Z2 symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 617-630.
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