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

M. Sabatini

Chaos, Solitons & Fractals, 2010, vol. 43, issue 1, 25-30

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].

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:43:y:2010:i:1:p:25-30

DOI: 10.1016/j.chaos.2010.07.002

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