Limit Cycles for two families of cubic systems
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Prohens, Rafel (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica)

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

DOI: 10.1016/j.na.2012.07.012

Postprint 23 p, 517.3 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
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