Invariant algebraic surfaces and hopf bifurcation of a finance model
Cândido, Murilo R. (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)

Date:	2018
Abstract:	Recently there are several works studying the finance model ẋ=z+x(y−a),ẏ=1−by−x2,ż=−x−cz, where a,b and c are positive parameters. The first objective of this paper is to show that this model exhibits one small-amplitude periodic solution emerging from a Hopf bifurcation at the equilibrium point (0, 1/b, 0) and in the second one we show that this system does not have invariant algebraic surfaces for any value of the parameters.
Grants:	Ministerio de Economía y Competitividad MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Darboux integrability ; Hopf bifurcation ; Averaging theory ; Invariant algebraic surface ; Lyapunov constant
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 28, Issue 12 (November 2018) , art. 1850150, ISSN 1793-6551

DOI: 10.1142/S021812741850150X

Postprint 15 p, 386.3 KB

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