Limit cycles in uniform isochronous centers of discontinuous differential systems with four zones
Itikawa, Jackson (Universidade de São Paulo. Instituto de Ciências Matemáticas e de Computação)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Mereu, Ana Cristina (Universidade Federal de São Carlos. Departamento de Física, Química e Matematica)
Oliveira, Regilene (Universidade de São Paulo. Instituto de Ciências Matemáticas e de Computação)

Date:	2017
Abstract:	We apply the averaging theory of first order for discontinuous differential systems to study the bifurcation of limit cycles from the periodic orbits of the uniform isochronous center of the differential systems ẋ = -y+x, y = x + xy, and ẋ = -y + xy, y = x + xy, when they are perturbed inside the class of all discontinuous quadratic and cubic polynomials differential systems with four zones separately by the axes of coordinates, respectively. Using averaging theory of first order the maximum number of limit cycles that we can obtain is twice the maximum number of limit cycles obtained in a previous work for discontinuous quadratic differential systems perturbing the same uniform isochronous quadratic center at origin perturbed with two zones separately by a straight line, and 5 more limit cycles than those achieved in a prior result for discontinuous cubic differential systems with the same uniform isochronous cubic center at the origin perturbed with two zones separately by a straight line. Comparing our results with those obtained perturbing the mentioned centers by the continuous quadratic and cubic differential systems we obtain 8 and 9 more limit cycles respectively.
Grants:	Ministerio de Economía y Competitividad MTM2016-77278-P Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 318999 European Commission 316338
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Limit cycle ; Averaging theory ; Uniform isochronous center ; Discontinuous polynomial system
Published in:	Discrete and continuous dynamical systems. Series B, Vol. 22, Issue 9 (November 2017) , p. 3259-3272, ISSN 1553-524X

DOI: 10.3934/dcdsb.2017136

Postprint 14 p, 332.1 KB

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