Bifurcation of limit cycles from a cubic reversible isochrone

2025/03/12 by Jihua Yang, Qipeng Zhang, Yang, Jihua +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2503.09004

openalex publication_date 2025/03/12 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to study the limit cycle problem of a cubic reversible system with an isochronous center, when it is perturbed inside a class of polynomials. An upper bound of the number of limit cycles is obtained using the Abelian integral. The algebraic structure of the Abelian integral is acquired thanks to some iterative formulas, which differs in many aspects from other methods. Some numerical simulations verify the existence of limit cycles.

Related

• Limit cycles appearing from the perturbation of a cubic isochronous center
• Bifurcation of limit cycles for a class of cubic Hamiltonian systems with nesting period annuli
• Limit cycles bifurcating from a degenerate center
• Bifurcation of limit cycles of the nongeneric quadratic reversible system with discontinuous perturbations
• Abelian integrals and limit cycles for a class of cubic polynomial vector fields of Lotka-Volterra type with a rational first integral of degree 2