Invariant algebraic surfaces and hopf bifurcation of a finance model

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,...

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Detalles Bibliográficos
Autores: Cândido, Murilo R.|||0000-0003-1360-2409, Llibre, Jaume|||0000-0002-9511-5999, Valls, Clàudia|||0000-0001-8279-1229
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:221360
Acceso en línea:https://ddd.uab.cat/record/221360
https://dx.doi.org/urn:doi:10.1142/S021812741850150X
Access Level:acceso abierto
Palabra clave:Darboux integrability
Hopf bifurcation
Averaging theory
Invariant algebraic surface
Lyapunov constant
Descripción
Sumario: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.