Limit cycles of a class of Liénard systems with restoring forces of seventh degree
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摘要
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.
论文关键词:16th Hilbert problem,Bifurcation,Limit cycle,Cuspidal loop,Liénard system
论文评审过程:Received 16 June 2016, Revised 13 June 2017, Accepted 4 August 2017, Available online 9 September 2017, Version of Record 9 September 2017.
论文官网地址:https://doi.org/10.1016/j.amc.2017.08.008