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)

Data:	2021
Resum:	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.
Ajuts:	Agencia Estatal de Investigación MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Averaging method ; 4-star-symmetry ; Hilbert's 16th problem ; Limit cycle bifurcation ; Piecewise polynomial system
Publicat a:	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

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