Dynamics of the polynomial differential systems with homogeneous nonlinearities and a star node
Bendjeddou, Ahmed (Université de Sétif(Algeria). Département de Mathématiques)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Salhi, Tayeb (Université de Bordj Bou Arréridj(Algeria). Département de Mathématiques)

Date:	2013
Abstract:	We consider the class of polynomial differential equations ˙x = λx + Pn(x, y), y˙ = λy + Qn(x, y), in R2 where Pn(x, y) and Qn(x, y) are homogeneous polynomials of degree n > 1 and λ ̸= 0, i. e. the class of polynomial differential systems with homogeneous nonlinearities with a star node at the origin. We prove that these systems are Darboux integrable. Moreover, for these systems we study the existence and non-existence of limit cycles surrounding the equilibrium point located at the origin.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 European Commission 316338 European Commission 318999
Note:	Agraïments: The first and third author is partially supported by the Algerian Ministry of Higher Education and Scientific Research.
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Star node ; Cubic system ; Limit cycle
Published in:	Journal of differential equations, Vol. 254 (2013) , p. 3530-3537, ISSN 1090-2732

DOI: 10.1016/j.jde.2013.01.032

Postprint 9 p, 771.8 KB

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