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

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

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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.



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

Como citar

Qualitative Theory Of Dynamical Systems. Basel: Springer Basel Ag, v. 13, n. 1, p. 129-148, 2014.