Global dynamics of a SD oscillator
Chen, Hebai (Fuzhou University. College of Mathematics and Computer Science)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Tang, Yilei (Shanghai Jiao Tong University. School of Mathematical Sciences)

Date:	2018
Abstract:	In this paper we derive the global bifurcation diagrams of a SD oscillator which exhibits both smooth and discontinuous dynamics depending on the value of a parameter a. We research all possible bifurcations of this system, including Pitchfork bifurcation, degenerate Hopf bifurcation, Homoclinic bifurcation, Double limit cycle bifurcation, Bautin bifurcation and Bogdanov-Takens bifurcation. Besides we prove that the system has at most five limit cycles. At last, we give all numerical phase portraits to illustrate our results.
Grants:	European Commission 655212 European Commission 318999 European Commission 316338 Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Averaging method ; Bogdanov-Takens bifurcation ; Homoclinic loop ; Hopf bifurcation ; Limit cycles ; SD oscillator
Published in:	Nonlinear dynamics, Vol. 91, issue 3 (Feb. 2018) , p. 1755-1777, ISSN 0924-090X

DOI: 10.1007/s11071-017-3979-y

Postprint 30 p, 1.1 MB

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