On the number of limit cycles for generic Lotka-Volterra system and Bogdanov-Takens system under perturbations of piecewise smooth polynomials

2018/05/26 by Shiyou Sui, Sui, Shiyou, Jihua Yang +3
Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1805.10446

openalex publication_date 2018/05/26 · openalex created_date 2018/06/01 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the bifurcation of limit cycles for generic L-V system (x=y+x²-y²±(4)/(√(3))xy,~y=-x+2xy) and B-T system (x=y,~y=-x+x²) under perturbations of piecewise smooth polynomials with degree n. Here the switching line is y=0. By using Picard-Fuchs equations, we bound the number of zeros of first order Melnikov function which controls the number of limit cycles bifurcating from the center. It is proved that the upper bounds of the number of limit cycles for generic L-V system and B-T system are respectively 36n-65~(n≥4),~37,57,93~(n=1,2,3) and 12n+6.

Citations

• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS

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