Bifurcation of limit cycles for a class of cubic Hamiltonian systems with nesting period annuli

2023/12/29 by Chang Yuan, Chang, Yuan, Liqin Zhao +3
Mathematics · Medicine · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2312.17466

openalex publication_date 2023/12/29 · openalex created_date 2024/01/02 · openalex updated_date 2026/07/28

Abstract

In this paper, we obtain the upper bound of the number of zeros of Abelian integral for a class of cubic Hamiltonian systems with nesting period annuli under perturbations of polynomials of degree n. Furthermore, we consider the Hopf and homoclinic bifurcation when a=-1,b=-2,c=1 and n=3, and obtain 18 distributions in which system has at least 3 limit cycles for each case.

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