Invariant algebraic surfaces and hopf bifurcation of a finance model

Murilo R. Cândido; Jaume Llibre; Claudia Valls

doi:10.1142/S021812741850150X

Invariant algebraic surfaces and hopf bifurcation of a finance model

Murilo R. Cândido, Jaume Llibre, Claudia Valls

Department of Mathematics

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8 Citations (Scopus)

Abstract

© 2018 World Scientific Publishing Company. Recently there are several works studying the finance model (equation presented), 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.

Original language	English
Article number	1850150
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	28
DOIs	https://doi.org/10.1142/S021812741850150X
Publication status	Published - 1 Nov 2018

Keywords

Darboux integrability
Hopf bifurcation
Lyapunov constant
averaging theory
invariant algebraic surface

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10.1142/S021812741850150X

https://ddd.uab.cat/record/221360

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title = "Invariant algebraic surfaces and hopf bifurcation of a finance model",

abstract = "{\textcopyright} 2018 World Scientific Publishing Company. Recently there are several works studying the finance model (equation presented), 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.",

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T1 - Invariant algebraic surfaces and hopf bifurcation of a finance model

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AU - Llibre, Jaume

AU - Valls, Claudia

PY - 2018/11/1

Y1 - 2018/11/1

N2 - © 2018 World Scientific Publishing Company. Recently there are several works studying the finance model (equation presented), 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.

AB - © 2018 World Scientific Publishing Company. Recently there are several works studying the finance model (equation presented), 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.

KW - Darboux integrability

KW - Hopf bifurcation

KW - Lyapunov constant

KW - averaging theory

KW - invariant algebraic surface

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U2 - 10.1142/S021812741850150X

DO - 10.1142/S021812741850150X

M3 - Article

SN - 0218-1274

VL - 28

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

M1 - 1850150

ER -

Invariant algebraic surfaces and hopf bifurcation of a finance model

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Keywords

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