{"title":"Limit cycles bifurcating from periodic integral manifold in non-smooth differential systems","authors":"Oscar A.R. Cespedes , Douglas D. Novaes","doi":"10.1016/j.physd.2025.134600","DOIUrl":null,"url":null,"abstract":"<div><div>This paper addresses the perturbation of higher-dimensional non-smooth autonomous differential systems characterized by two zones separated by a codimension-one manifold, with an integral manifold foliated by crossing periodic solutions. Our primary focus is on developing the Melnikov method to analyze the emergence of limit cycles originating from the periodic integral manifold. While previous studies have explored the Melnikov method for autonomous perturbations of non-smooth differential systems with a linear switching manifold and with a periodic integral manifold, either open or of codimension 1, our work extends to non-smooth differential systems with a non-linear switching manifold and more general periodic integral manifolds, where the persistence of periodic orbits is of interest. We illustrate our findings through several examples, highlighting the applicability and significance of our main result.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134600"},"PeriodicalIF":2.7000,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica D: Nonlinear Phenomena","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S016727892500079X","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This paper addresses the perturbation of higher-dimensional non-smooth autonomous differential systems characterized by two zones separated by a codimension-one manifold, with an integral manifold foliated by crossing periodic solutions. Our primary focus is on developing the Melnikov method to analyze the emergence of limit cycles originating from the periodic integral manifold. While previous studies have explored the Melnikov method for autonomous perturbations of non-smooth differential systems with a linear switching manifold and with a periodic integral manifold, either open or of codimension 1, our work extends to non-smooth differential systems with a non-linear switching manifold and more general periodic integral manifolds, where the persistence of periodic orbits is of interest. We illustrate our findings through several examples, highlighting the applicability and significance of our main result.
期刊介绍:
Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.