Periodic Orbits Bifurcating from a Nonisolated Zero-Hopf Equilibrium of Three-Dimensional Differential Systems Revisited

Murilo R. Cândido; Jaume Llibre

doi:https://doi.org/10.1142/S021812741850058X

Periodic Orbits Bifurcating from a Nonisolated Zero-Hopf Equilibrium of Three-Dimensional Differential Systems Revisited

Murilo R. Cândido, Jaume Llibre

Department of Mathematics

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

3 Citations (Scopus)

Abstract

© 2018 World Scientific Publishing Company. In this paper, we study the periodic solutions bifurcating from a nonisolated zero-Hopf equilibrium in a polynomial differential system of degree two in ℝ3. More specifically, we use recent results of averaging theory to improve the conditions for the existence of one or two periodic solutions bifurcating from such a zero-Hopf equilibrium. This new result is applied for studying the periodic solutions of differential systems in ℝ3 having n-scroll chaotic attractors.

Original language	English
Article number	1850058
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	28
Issue number	5
DOIs	https://doi.org/10.1142/S021812741850058X
Publication status	Published - 1 May 2018

Keywords

Averaging theory
periodic solutions
polynomial differential systems
zero-Hopf bifurcation
zero-Hopf equilibrium

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https://ddd.uab.cat/record/199371

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AB - © 2018 World Scientific Publishing Company. In this paper, we study the periodic solutions bifurcating from a nonisolated zero-Hopf equilibrium in a polynomial differential system of degree two in ℝ3. More specifically, we use recent results of averaging theory to improve the conditions for the existence of one or two periodic solutions bifurcating from such a zero-Hopf equilibrium. This new result is applied for studying the periodic solutions of differential systems in ℝ3 having n-scroll chaotic attractors.

KW - Averaging theory

KW - periodic solutions

KW - polynomial differential systems

KW - zero-Hopf bifurcation

KW - zero-Hopf equilibrium

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Periodic Orbits Bifurcating from a Nonisolated Zero-Hopf Equilibrium of Three-Dimensional Differential Systems Revisited

Abstract

Keywords

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