Web of Science: 3 citations, Scopus: 3 citations, Google Scholar: citations
Limit cycles of piecewise polynomial differential systems with the discontinuity line xy = 0
Li, Tao (Southwestern University of Finance and Economics. School of Economic Mathematics (China))
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date: 2021
Abstract: In this paper we study the maximum number of limit cycles bifurcating from the periodic orbits of the center x. = −y((x + y)/2), y. = x((x + y)/2) with m ≥ 0 under discontinuous piecewise polynomial (resp. polynomial Hamiltonian) perturbations of degree n with the discontinuity set {(x, y) ∈ R : xy = 0}. Using the averaging theory up to any order N, we give upper bounds for the maximum number of limit cycles in the function of m, n, N. More importantly, employing the higher order averaging method we provide new lower bounds of the maximum number of limit cycles for several types of piecewise polynomial systems, which improve the results of the previous works. Besides, we explore the effect of 4-star-symmetry on the maximum number of limit cycles bifurcating from the unperturbed periodic orbits. Our result implies that 4-star-symmetry almost halves the maximum number.
Grants: Agencia Estatal de Investigación MTM2016-77278-P
Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617
European Commission 777911
Rights: Tots els drets reservats.
Language: Anglès
Document: Article ; recerca ; Versió acceptada per publicar
Subject: Averaging method ; 4-star-symmetry ; Hilbert's 16th problem ; Limit cycle bifurcation ; Piecewise polynomial system
Published in: Communications on pure & applied analysis, Vol. 20, Issue 11 (November 2021) , p. 3887-3909, ISSN 1553-5258

DOI: 10.3934/cpaa.2021136


Postprint
13 p, 856.4 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles

 Record created 2022-03-18, last modified 2023-06-16



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