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

Llibre, Jaume; Lopes, Bruno D.; De Moraes, Jaime R. [UNESP]

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

Data

2014-04-01

Autores

Llibre, Jaume

Lopes, Bruno D.

De Moraes, Jaime R.

Editor

Springer

Tipo

Artigo

Direito de acesso

Acesso restrito

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.