Limit Cycles Bifurcating from the Periodic Orbits of a Discontinuous Piecewise Linear Differentiable Center with Two Zones

Autor(es)

Llibre, Jaume ^[1] ; Novaes, Douglas D. ^[2] ; Teixeira, Marco A. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia - Spain

^[2] Univ Estadual Campinas, Dept Matemat, BR-13083859 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS; v. 25, n. 11 OCT 2015.
• Citações Web of Science: 8

Resumo

We study a class of discontinuous piecewise linear differential systems with two zones separated by the straight line x = 0. In x > 0, we have a linear saddle with its equilibrium point living in x > 0, and in x < 0 we have a linear differential center. Let p be the equilibrium point of this linear center, when p lives in x < 0, we say that it is real, and when p lives in x > 0 we say that it is virtual. We assume that this discontinuous piecewise linear differential system formed by the center and the saddle has a center q surrounded by periodic orbits ending in a homoclinic orbit of the saddle, independent if p is real, virtual or p is in x = 0. Note that q = p if p is real or p is in x = 0. We perturb these three classes of systems, according to the position of p, inside the class of all discontinuous piecewise linear differential systems with two zones separated by x = 0. Let N be the maximum number of limit cycles which can bifurcate from the periodic solutions of the center q with these perturbations. Our main results show that N = 2 when p is on x = 0, and N >= 2 when p is a real or virtual center. Furthermore, when p is a real center we found an example satisfying N >= 3. (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: 13/16492-0 - Método Averaging para o estudo de soluções periódicas de equações diferenciais e suas aplicações
• Beneficiário: Douglas Duarte Novaes
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Doutorado