Limit cycles via higher order perturbations for some piecewise differential systems

Autor(es)

Buzzi, Claudio A. ^[1] ; Silva Lima, Mauricio Firmino ^[2] ; Torregrosa, Joan ^[3]

Afiliação do(s) autor(es)

^[1] Univ Estadual Paulista, Dept Matemat, Sao Jose Do Rio Preto - Brazil

^[2] Univ Fed ABC, Ctr Matemat Comp & Cognicao, BR-09210170 Santo Andre, SP - Brazil

^[3] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona - Spain

• Tipo de documento: Artigo Científico
• Fonte: PHYSICA D-NONLINEAR PHENOMENA; v. 371, p. 28-47, MAY 15 2018.
• Citações Web of Science: 0

Resumo

A classical perturbation problem is the polynomial perturbation of the harmonic oscillator, (x', y') = (-y + epsilon f(x, y, epsilon), x + epsilon g(x, y, epsilon)). In this paper we study the limit cycles that bifurcate from the period annulus via piecewise polynomial perturbations in two zones separated by a straight line. We prove that, for polynomial perturbations of degree n, no more than Nn-1 limit cycles appear up to a study of order N. We also show that this upper bound is reached for orders one and two. Moreover, we study this problem in some classes of piecewise Lienard differential systems providing better upper bounds for higher order perturbation in 8, showing also when they are reached. The Poincare-Pontryagin-Melnikov theory is the main technique used to prove all the results. (C) 2018 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 17/03352-6 - Ciclos limites em alguns sistemas diferenciais suaves por partes
• Beneficiário: Claudio Aguinaldo Buzzi
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional
• Processo FAPESP: 12/18780-0 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Marco Antônio Teixeira
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 13/24541-0 - Teorias ergódica e qualitativa dos sistemas dinâmicos
• Beneficiário: Claudio Aguinaldo Buzzi
• Modalidade de apoio: Auxílio à Pesquisa - Temático