Limit cycles bifurcating from periodic integral manifold in non-smooth differential systems

IF 2.7 3区 数学 Q1 MATHEMATICS, APPLIED
Oscar A.R. Cespedes , Douglas D. Novaes
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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.
非光滑微分系统中周期积分流形分叉的极限环
本文研究了一类高维非光滑自治微分系统的摄动问题,该系统的两个区域由一个协维一流形分隔,其中一个积分流形由交叉周期解叶化。我们的主要重点是发展Melnikov方法来分析源自周期积分流形的极限环的出现。虽然以前的研究已经探索了Melnikov方法用于具有线性开关流形和周期积分流形的非光滑微分系统的自治摄动,无论是开放的还是余维为1的,我们的工作扩展到具有非线性开关流形和更一般的周期积分流形的非光滑微分系统,其中周期轨道的持续性是感兴趣的。我们通过几个例子来说明我们的发现,突出了我们的主要结果的适用性和意义。
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来源期刊
Physica D: Nonlinear Phenomena
Physica D: Nonlinear Phenomena 物理-物理:数学物理
CiteScore
7.30
自引率
7.50%
发文量
213
审稿时长
65 days
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.
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