On the dynamics of a system that bridges the gap between Lorenz and Chen systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Rodrigues, Ana (University of Exeter. College of Engineering, Mathematics and Physics)

Date:	2015
Abstract:	A one-parameter family of differential systems that bridges the gap between the Lorenz and the Chen systems was proposed by Lu, Chen, Cheng and Celikovsy. The goal of this paper is to analyze what we can say using analytic tools about the dynamics of this one-parameter family of differential systems. We shall describe its global dynamics at infinity, and for two special values of the parameter a we also can describe the global dynamics in the whole R 3 using the invariant algebraic surfaces of the family. Additionally we characterize the Hopf bifurcations of this family.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 318999
Note:	Agraïments: FEDER-UNAB 10-4E-378. The second author was supported by the Swedish Research Council VR Grant 2010/5905.
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Hopf bifurcation ; Invariant algebraic surface ; Lorenz-Chen system ; Poincaré compactification
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 25 Núm. 9 (2015) , p. 1550122 (9 pages), ISSN 1793-6551

DOI: 10.1142/S0218127415501229

Postprint 14 p, 765.8 KB

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