Melnikov analysis for planar piecewise linear vector fields with algebraic switching curve yⁿ-x^m=0

2022/02/06 by Cintia C. Santos, Santos, Cintia C., Oscar A. R. Cespedes +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2202.02846

openalex publication_date 2022/02/06 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to the study of the maximum number of limit cycles, H(m,n), of a planar piecewise linear differential system with two zones separated by the curve yⁿ-x^m=0, with n,m being positive integers. More precisely, we provide a lower estimate of H(m,n). for all m,n∈ ℕ, for piecewise linear perturbations of the linear center using some recent results about Chebyshev systems with positive accuracy and Melnikov Theory

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