On the dynamics of a model with coexistence of three attractors: a point, a periodic orbit and a strange attractor
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemàtica)

Date:	2017
Abstract:	For a dynamical system described by a set of autonomous differential equations, an attractor can be either a point, or a periodic orbit, or even a strange attractor. Recently a new chaotic system with only one parameter has been presented where besides a point attractor and a chaotic attractor, it also has a coexisting attractor limit cycle which makes evident the complexity of such a system. We study using analytic tools the dynamics of such system. We describe its global dynamics at infinity, and show that it has no Darboux first integrals. Additionally, we characterize its Hopf bifurcations.
Grants:	European Commission 318999 European Commission 316338 Ministerio de Economía y Competitividad MTM2013-40998-P Ministerio de Economía y Competitividad UNAB13-4E-1604 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568
Note:	The second author is partially supported by FCT/Portugal through UID/MAT/04459/2013.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Chaotic system ; Darboux integrability ; Hopf bifurcation ; Poincaré compactification
Published in:	Mathematical Physics, Analysis and Geometry, Vol. 20 Núm. 2 (2017) , p. 1-12, ISSN 1572-9656

DOI: 10.1007/s11040-017-9240-6

Postprint 14 p, 310.6 KB

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