Web of Science: 20 citations, Scopus: 25 citations, Google Scholar: citations
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.
Rights: Tots els drets reservats.
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

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles

 Record created 2016-05-06, last modified 2022-07-13



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