On the dynamics of a model with coexistence of three attractors: a point, a periodic orbit and a strange attractor

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 a...

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Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Valls, Clàudia|||0000-0001-8279-1229
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:182494
Acceso en línea:https://ddd.uab.cat/record/182494
https://dx.doi.org/urn:doi:10.1007/s11040-017-9240-6
Access Level:acceso abierto
Palabra clave:Chaotic system
Darboux integrability
Hopf bifurcation
Poincaré compactification
Descripción
Sumario: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.