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

作者：Llibre Jaume^*; Lopes Bruno D; De Moraes Jaime R

来源：Qualitative Theory of Dynamical Systems, 2014, 13(1): 129-148.

DOI：10.1007/s12346-014-0109-9

• Polynomial vector field
• Limit cycle
• Averaging method
• Periodic orbit
• Isochronous center

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.

• 出版日期2014-4
• 单位Univ Estadual Paulista