Home > Articles > Published articles > Limit Cycles for two families of cubic systems |
Date: | 2012 |
Abstract: | In this paper we study the number of limit cycles of two families of cubic systems introduced in previous papers to model real phenomena. The first one is motivated by a model of star formation histories in giant spiral galaxies and the second one comes from a model of Volterra type. To prove our results we develop a new criterion on non-existence of periodic orbits and we extend a well-known criterion on uniqueness of limit cycles due to Kuang and Freedman. Both results allow to reduce the problem to the control of the sign of certain functions that are treated by algebraic tools. Moreover, in both cases, we prove that when the limit cycles exist they are non-algebraic. |
Grants: | Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Cubic system ; Kolmogorov system ; Limit cycle ; Bifurcation |
Published in: | Nonlinear Analysis : Theory, Methods and Applications, Vol. 75 (2012) , p. 6402-6417, ISSN 0362-546X |
Postprint 23 p, 517.3 KB |