Limit Cycles for a Class of Continuous and Discontinuous Cubic Polynomial Differential Systems

Autor(es)

Llibre, Jaume ^[1] ; Lopes, Bruno D. ^[2] ; De Moraes, Jaime R. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Autonoma Barcelona. Dept Matemat

^[2] Univ Autonoma Barcelona. Dept Matemat

^[3] Univ Estadual Paulista. IBILCE

• Tipo de documento: Artigo Científico
• Fonte: Qualitative Theory of Dynamical Systems; v. 13, n. 1, p. 129-148, APR 2014.
• Citações Web of Science: 0

Resumo

We study the maximum number of limit cycles that bifurcate from the periodic solutions of the family of isochronous cubic polynomial centers (x) over dot = y(-1 + 2 alpha x + 2 beta x(2)), (y) over dot = x + alpha(y(2) - x(2)) + 2 beta xy(2), alpha is an element of R, beta < 0, when it is perturbed inside the classes of all continuous and discontinuous cubic polynomial differential systems with two zones of discontinuity separated by a straight line. We obtain that this number is 3 for the perturbed continuous systems and at least 12 for the discontinuous ones using the averaging method of first order. (AU)

• Processo FAPESP: 10/17956-1 - Conjuntos Minimais de Sistemas Lineares por Partes
• Beneficiário: Jaime Rezende de Moraes
• Modalidade de apoio: Bolsas no Brasil - Doutorado