On the number of limit cycles bifurcating from the linear center with an algebraic switching curve

2020/12/07 by Jiaxin Wang, Jinping Zhou, Wang, Jiaxin +3
Mathematics · Medicine · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2012.03566

openalex publication_date 2020/12/07 · openalex created_date 2022/11/30 · openalex updated_date 2026/07/28

Abstract

This paper studies the family of piecewise linear differential systems in the plane with two pieces separated by a switching curve y=x^m, where m>1 is an arbitrary positive. By analysing the first order Melnikov function, we give an upper bound and an lower bound of the maximum number of limit cycles which bifurcate from the period annulus around the origin under polynomial perturbations of degree n. The results shows that the degree of switching curves affect the number of limit cycles.

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