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

Junmin Yang and Wei Ding

Applied Mathematics and Computation, 2018, vol. 316, issue C, 422-437

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.

Keywords: 16th Hilbert problem; Bifurcation; Limit cycle; Cuspidal loop; Liénard system (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:316:y:2018:i:c:p:422-437

DOI: 10.1016/j.amc.2017.08.008

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