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

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

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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):	Llibre, Jaume ^[1] ; Lopes, Bruno D. ^[2] ; De Moraes, Jaime R. ^[3] Total Authors: 3
Affiliation:	^[1] Univ Autonoma Barcelona. Dept Matemat ^[2] Univ Autonoma Barcelona. Dept Matemat ^[3] Univ Estadual Paulista. IBILCE Total Affiliations: 3
Document type:	Journal article
Source:	Qualitative Theory of Dynamical Systems; v. 13, n. 1, p. 129-148, APR 2014.
Web of Science Citations:	0
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. (AU)

FAPESP's process:	10/17956-1 - Minimal Sets of Piecewise Linear Systems
Grantee:	Jaime Rezende de Moraes
Support Opportunities:	Scholarships in Brazil - Doctorate

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