An estimation for the number of limit cycles in a Lienard-like perturbation of a quadratic nonlinear center

Autor(es)

Martins, Ricardo Miranda ^[1] ; Mereu, Ana Cristina ^[2] ; Oliveira, Regilene D. S. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, IMECC, Dept Math, BR-13083859 Campinas, SP - Brazil

^[2] Univ Fed Sao Carlos, Dept Phys Chem & Math, BR-18052780 Sorocaba, SP - Brazil

^[3] Univ Sao Paulo, ICMC, Dept Math, BR-13566590 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: NONLINEAR DYNAMICS; v. 79, n. 1, p. 185-194, JAN 2015.
• Citações Web of Science: 3

Resumo

The number of limit cycles which bifurcates from periodic orbits of a differential system with a center has been extensively studied recently using many distinct tools. This problem was proposed by Hilbert in 1900, and it is a difficult problem, so only particular families of such systems were considered. In this paper, we study the maximum number of limit cycles that can bifurcate from an integrable nonlinear quadratic isochronous center, when perturbed inside a class of Lienard-like polynomial differential systems of arbitrary degree n. We apply the averaging theory of first order to this class of Lienard-like polynomial differential systems, and we estimate that the number of limit cycles is 2{[}(n - 2)/2], where {[}.] denotes the integer part function. (AU)

• 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: 12/06879-1 - Sistemas dinâmicos descontínuos: teoria qualitativa e estabilidade estrutural
• Beneficiário: Ricardo Miranda Martins
• Modalidade de apoio: Auxílio à Pesquisa - Regular