Home > Articles > Published articles > Dynamics of the polynomial differential systems with homogeneous nonlinearities and a star node |
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 |
Postprint 9 p, 771.8 KB |