Limit Cycles for a Class of Continuous and Discontinuous Cubic Polynomial Differential Systems
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Springer
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Abstract
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.
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Keywords
Polynomial vector field, Limit cycle, Averaging method, Periodic orbit, Isochronous center
Language
English
Citation
Qualitative Theory Of Dynamical Systems. Basel: Springer Basel Ag, v. 13, n. 1, p. 129-148, 2014.
