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On the number of limit cycles of a pendulum-like equation with two switching lines

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  • Yang, Jihua

Abstract

This paper is devoted to study the limit cycle bifurcations of a pendulum equation x˙=y,y˙=−sinx under non-smooth perturbations of polynomials of cosx, sinx and y of degree n with switching lines x=0 and y=0. The upper bounds of the number of limit cycles in both the oscillatory and the rotary regions are obtained by expressing the corresponding first order Melnikov functions as several generating functions, some of which are complete elliptic integrals of the first and second kind.

Suggested Citation

  • Yang, Jihua, 2021. "On the number of limit cycles of a pendulum-like equation with two switching lines," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s096007792100446x
    DOI: 10.1016/j.chaos.2021.111092
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    References listed on IDEAS

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    1. Wang, Yanqin & Han, Maoan & Constantinescu, Dana, 2016. "On the limit cycles of perturbed discontinuous planar systems with 4 switching lines," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 158-177.
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