Melnikov functions of arbitrary order for piecewise smooth differential systems in \(\mathbb{R}^n\) and applications
type: Item
instance of: scholarly article
title: Melnikov functions of arbitrary order for piecewise smooth differential systems in \(\mathbb{R}^n\) and applications
zbMATH Open document ID: 1495.34026
author: Xingwu Chen
author: Tao Li
author: Jaume Llibre
published in: Journal of Differential Equations
publication date: 2022-02-10T00:00:00Z
review text: The authors investigate limit cycles bifurcating from periodic submanifold of \(n\)-dimensonal piecewise smooth dynamical systems with two zones separated by a hyperplane. In order to obtain the maximum number of limit cycles, they obtain arbitrary order Melnikov function by using Faá di Bruno's Formula. As applications, they study the maximum number of crossing limit cycles bifurcating from an \(n\)-dimensional periodic submanifold caused by non-smooth centers of fold-fold type and perturbations of piecewise smooth Hamiltonian systems. Moreover, they prove that these upper bounds can be reached. Their main results extend some known results in these directions.
reviewed by: Dingheng Pi
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 34E10
zbMATH DE Number: 7471754
zbMATH Keywords: Melnikov theory
zbMATH Keywords: Hilbert's 16th problem
zbMATH Keywords: fold-fold singularity
zbMATH Keywords: limit cycle bifurcation
zbMATH Keywords: piecewise smooth differential system
MaRDI profile type: Publication
full work available at URL: j.jde.2022.01.019
OpenAlex ID: W4205903613
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DOI: 10.1016/J.JDE.2022.01.019
description: scientific article; zbMATH DE number 7471754