Home > Articles > Published articles > On the number of limit cycles of a class of polynomial differential systems |
Date: | 2012 |
Abstract: | We study the number of limit cycles of the polynomial differential systems of the form x˙ = y − g1(x) − f1(x)y, y˙ = −x − g2(x) − f2(x)y, where g1, f1, g2 and f2 are polynomials of a given degree. Note that when g1(x) = f1(x) = 0 we obtain the generalized polynomial Li'enard differential systems. We provide an accurate upper bound of the maximum number of limit cycles that the above system can have bifurcating from the periodic orbits of the linear center ˙x = y, ˙y = −x using the averaging theory of first and second order. |
Grants: | Ministerio de Educación y Ciencia MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 |
Note: | Agraïments: The second author has been partially supported by FCT through CAMGSD. |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Limit cycles ; Polynomial differential systems |
Published in: | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012, p. 1-14, ISSN 1471-2946 |
Postprint 13 p, 605.3 KB |