On the Dynamics of the Unified Chaotic System between Lorenz and Chen Systems

Jaume Llibre; Ana Rodrigues

doi:https://doi.org/10.1142/S0218127415501229

On the Dynamics of the Unified Chaotic System between Lorenz and Chen Systems

Jaume Llibre, Ana Rodrigues

Department of Mathematics

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

5 Citations (Scopus)

Abstract

© 2015 World Scientific Publishing Company. A one-parameter family of differential systems that bridges the gap between the Lorenz and the Chen systems was proposed by Lu, Chen, Cheng and Celikovsy. The goal of this paper is to analyze what we can say using analytic tools about the dynamics of this one-parameter family of differential systems. We shall describe its global dynamics at infinity, and for two special values of the parameter a we can also describe the global dynamics in the whole R3 using the invariant algebraic surfaces of the family. Additionally we characterize the Hopf bifurcations of this family.

Original language	English
Article number	1550122
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	25
Issue number	9
DOIs	https://doi.org/10.1142/S0218127415501229
Publication status	Published - 8 Aug 2015

Keywords

Chen system
Hopf bifurcation
Lorenz system
Poincaré compactification
invariant algebraic surface
unified chaotic system

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https://ddd.uab.cat/record/145306

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title = "On the Dynamics of the Unified Chaotic System between Lorenz and Chen Systems",

abstract = "{\textcopyright} 2015 World Scientific Publishing Company. A one-parameter family of differential systems that bridges the gap between the Lorenz and the Chen systems was proposed by Lu, Chen, Cheng and Celikovsy. The goal of this paper is to analyze what we can say using analytic tools about the dynamics of this one-parameter family of differential systems. We shall describe its global dynamics at infinity, and for two special values of the parameter a we can also describe the global dynamics in the whole R3 using the invariant algebraic surfaces of the family. Additionally we characterize the Hopf bifurcations of this family.",

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AU - Llibre, Jaume

AU - Rodrigues, Ana

PY - 2015/8/8

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N2 - © 2015 World Scientific Publishing Company. A one-parameter family of differential systems that bridges the gap between the Lorenz and the Chen systems was proposed by Lu, Chen, Cheng and Celikovsy. The goal of this paper is to analyze what we can say using analytic tools about the dynamics of this one-parameter family of differential systems. We shall describe its global dynamics at infinity, and for two special values of the parameter a we can also describe the global dynamics in the whole R3 using the invariant algebraic surfaces of the family. Additionally we characterize the Hopf bifurcations of this family.

AB - © 2015 World Scientific Publishing Company. A one-parameter family of differential systems that bridges the gap between the Lorenz and the Chen systems was proposed by Lu, Chen, Cheng and Celikovsy. The goal of this paper is to analyze what we can say using analytic tools about the dynamics of this one-parameter family of differential systems. We shall describe its global dynamics at infinity, and for two special values of the parameter a we can also describe the global dynamics in the whole R3 using the invariant algebraic surfaces of the family. Additionally we characterize the Hopf bifurcations of this family.

KW - Chen system

KW - Hopf bifurcation

KW - Lorenz system

KW - Poincaré compactification

KW - invariant algebraic surface

KW - unified chaotic system

U2 - https://doi.org/10.1142/S0218127415501229

DO - https://doi.org/10.1142/S0218127415501229

M3 - Article

VL - 25

IS - 9

M1 - 1550122

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On the Dynamics of the Unified Chaotic System between Lorenz and Chen Systems

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Keywords

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