一类四次扰动Liénard系统的极限环分支

Abstract

Abstract:

In this paper, we study the number of limit cycles by Poincaré bifurcation for some Liénard system of degree 4. We prove that the system can bifurcate at most 6 limit cycles from the periodic annulus, by the tools of regular chain theory in polynomial algebra and Chebyshev criteria, at least 3 limit cycles by asymptotic expansions of the related Abelian integral (first order Melnikov functions).

Key words: Liénard system, Chebyshev system, Melnikov functions, Weak Hilbert's 16th problem

CLC Number:

O175.12

Hongying Zhu,Minzhi Wei,Sumin Yang,Caoqing Jiang. Bifurcation of Limit Cycles from a Liénard System of Degree 4[J].Acta mathematica scientia,Series A, 2021, 41(4): 936-953.

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Bifurcation of Limit Cycles from a Liénard System of Degree 4

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