On the limit cycles of the polynomial differential systems with a linear node and homogeneous nonlinearities
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Yu, Jiang (Shanghai Jiao Tong University. Department of Mathematics)
Zhang, Xiang (Shanghai Jiao Tong University. Department of Mathematics)

Date:	2014
Abstract:	We consider the class of polynomial differential equations ˙x = λx + Pn(x, y), y˙ = µy + Qn(x, y) in R2 where Pn(x, y) and Qn(x, y) are homogeneous polynomials of degree n > 1 and λ 6= µ, i. e. the class of polynomial differential systems with a linear node with different eigenvalues and homogeneous nonlinearities. For this class of polynomial differential equations we study the existence and non-existence of limit cycles surrounding the node localized at the origin of coordinates.
Grants:	Ministerio de Ciencia e Innovación MTM 2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 European Commission 318999 European Commission 316338
Note:	Agraïments: The second author is partially supported by NNSF of China grant number 10971133. The third author is partially supported by NNSF of China grant number 11271252 and RFDP of Higher Education of China grant 20110073110054. The first and third authors are also supported by FP7-PEOPLE-2012-IRSES-316338 of Europe.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Homogeneous nonlinearities ; Limit cycles
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 24 Núm. 5 (2014) , p. 1450065, ISSN 1793-6551

DOI: 10.1142/S0218127414500655

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