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Limit cycles of a class of Liénard systems with restoring forces of seventh degree

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  • Yang, Junmin
  • Ding, Wei

Abstract

The study of limit cycles for Liénard system is very important not only in theoretical studies but also in applications. In this paper, we study the number of limit cycles for a class of Liénard systems with restoring forces of seventh degree. Let H(n, m) denote the maximum number of limit cycles bifurcated from the generalized Liénard system x˙=y,y˙=−g(x)−f(x)y, where f(x) and g(x) are polynomials in x and degf=n,detg=m. We greatly improve the existing results of H(n, m) for m=7,n=4 and m=7,n=2n¯ with 4≤n¯≤20.

Suggested Citation

  • Yang, Junmin & Ding, Wei, 2018. "Limit cycles of a class of Liénard systems with restoring forces of seventh degree," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 422-437.
    • Handle: RePEc:eee:apmaco:v:316:y:2018:i:c:p:422-437
    DOI: 10.1016/j.amc.2017.08.008
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    References listed on IDEAS

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    1. Sun, Xianbo, 2015. "Multiple limit cycles of some strongly nonlinear Liénard–Van der Pol oscillator," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 620-630.
    2. Asheghi, R. & Bakhshalizadeh, A., 2015. "Limit cycles in a Liénard system with a cusp and a nilpotent saddle of order 7," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 120-128.
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    Cited by:

    1. Yuanyuan Tian & Jing Li, 2019. "Periodic Solutions for a Four-Dimensional Coupled Polynomial System with N-Degree Homogeneous Nonlinearities," Mathematics, MDPI, vol. 7(12), pages 1-21, December.

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