具有尖点环的非光滑微分系统的极限环分支

Abstract

Abstract:

This paper studies the limit cycle bifurcation problem of a non-smooth differential system with a cuspidal loop under non-smooth perturbation of polynomials of degree $n$. Firstly, the first order Melnikov function $M(h)$ of the perturbed differential system is expressed as a linear combination of several generating integrals with polynomial coefficients, and the independence of coefficients of these polynomials is proved by mathematical induction. Then the lower bounds of the number of limit cycles bifurcating the origin and cuspidal loop are obtained by using the asymptotic expansions of $M(h)$.

Key words: Limit cycle, Melnikov function, Cuspidal loop, Asymptotic expansion

CLC Number:

O175.12

Yang Jihua, Ma Liang. Limit Cycle Bifurcations of a Non-smooth Differential System with a Cuspidal Loop[J].Acta mathematica scientia,Series A, 2023, 43(6): 1667-1680.

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Limit Cycle Bifurcations of a Non-smooth Differential System with a Cuspidal Loop

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