On the integrability and the zero-Hopf bifurcation of a Chen–Wang differential system

Jaume Llibre; Regilene D.S. Oliveira; Claudia Valls

doi:https://doi.org/10.1007/s11071-014-1873-4

On the integrability and the zero-Hopf bifurcation of a Chen–Wang differential system

Jaume Llibre, Regilene D.S. Oliveira, Claudia Valls

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

14 Citations (Scopus)

Abstract

© 2015, Springer Science+Business Media Dordrecht. The first objective of this paper was to study the Darboux integrability of the polynomial differential system (Formula presented)and the second one is to show that for (Formula presented) sufficiently small this model exhibits two small amplitude periodic solutions that bifurcate from a zero-Hopf equilibrium point localized at the origin of coordinates when (Formula presented). We note that this polynomial differential system introduced by Chen and Wang (Nonlinear Dyn 71:429–436, 2013) is relevant in the sense that it is the first system in (Formula presented) exhibiting chaotic motion without having equilibria.

Original language	English
Pages (from-to)	353-361
Journal	Nonlinear Dynamics
Volume	80
Issue number	1-2
DOIs	https://doi.org/10.1007/s11071-014-1873-4
Publication status	Published - 1 Jan 2015

Keywords

Averaging theory
Darboux integrability
Zero-Hopf bifurcation

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AU - Oliveira, Regilene D.S.

AU - Valls, Claudia

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AB - © 2015, Springer Science+Business Media Dordrecht. The first objective of this paper was to study the Darboux integrability of the polynomial differential system (Formula presented)and the second one is to show that for (Formula presented) sufficiently small this model exhibits two small amplitude periodic solutions that bifurcate from a zero-Hopf equilibrium point localized at the origin of coordinates when (Formula presented). We note that this polynomial differential system introduced by Chen and Wang (Nonlinear Dyn 71:429–436, 2013) is relevant in the sense that it is the first system in (Formula presented) exhibiting chaotic motion without having equilibria.

KW - Averaging theory

KW - Darboux integrability

KW - Zero-Hopf bifurcation

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