Dynamic Analysis of a Lü Model in Six Dimensions and Its Projections

Luis Alberto Quezada-Téllez; Salvador Carrillo-Moreno; Oscar Rosas-Jaimes; José Job Flores-Godoy; Guillermo Fernández-Anaya

doi:10.1515/ijnsns-2016-0076

Dynamic Analysis of a Lü Model in Six Dimensions and Its Projections

Luis Alberto Quezada-Téllez, Salvador Carrillo-Moreno, Oscar Rosas-Jaimes, José Job Flores-Godoy, Guillermo Fernández-Anaya

Department of Natural Sciences

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

10 Scopus citations

Abstract

In this article, extended complex Lü models (ECLMs) are proposed. They are obtained by substituting the real variables of the classical Lü model by complex variables. These projections, spaning from five dimensions (5D) and six dimensions (6D), are studied in their dynamics, which include phase spaces, calculations of eigenvalues and Lyapunov's exponents, Poincaré maps, bifurcation diagrams, and related analyses. It is shown that in the case of a 5D extension, we have obtained chaotic trajectories; meanwhile the 6D extension shows quasiperiodic and hyperchaotic behaviors and it exhibits strange nonchaotic attractor (SNA) features.

Original language	English
Pages (from-to)	371-384
Number of pages	14
Journal	International Journal of Nonlinear Sciences and Numerical Simulation
Volume	18
Issue number	5
DOIs	https://doi.org/10.1515/ijnsns-2016-0076
State	Published - 26 Jul 2017

Keywords

Lü model
complex variable
hyperchaotic systems
lyapunov exponents
stability

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abstract = "In this article, extended complex L{\"u} models (ECLMs) are proposed. They are obtained by substituting the real variables of the classical L{\"u} model by complex variables. These projections, spaning from five dimensions (5D) and six dimensions (6D), are studied in their dynamics, which include phase spaces, calculations of eigenvalues and Lyapunov's exponents, Poincar{\'e} maps, bifurcation diagrams, and related analyses. It is shown that in the case of a 5D extension, we have obtained chaotic trajectories; meanwhile the 6D extension shows quasiperiodic and hyperchaotic behaviors and it exhibits strange nonchaotic attractor (SNA) features.",

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AU - Alberto Quezada-Téllez, Luis

AU - Carrillo-Moreno, Salvador

AU - Rosas-Jaimes, Oscar

AU - Flores-Godoy, José Job

AU - Fernández-Anaya, Guillermo

PY - 2017/7/26

Y1 - 2017/7/26

N2 - In this article, extended complex Lü models (ECLMs) are proposed. They are obtained by substituting the real variables of the classical Lü model by complex variables. These projections, spaning from five dimensions (5D) and six dimensions (6D), are studied in their dynamics, which include phase spaces, calculations of eigenvalues and Lyapunov's exponents, Poincaré maps, bifurcation diagrams, and related analyses. It is shown that in the case of a 5D extension, we have obtained chaotic trajectories; meanwhile the 6D extension shows quasiperiodic and hyperchaotic behaviors and it exhibits strange nonchaotic attractor (SNA) features.

AB - In this article, extended complex Lü models (ECLMs) are proposed. They are obtained by substituting the real variables of the classical Lü model by complex variables. These projections, spaning from five dimensions (5D) and six dimensions (6D), are studied in their dynamics, which include phase spaces, calculations of eigenvalues and Lyapunov's exponents, Poincaré maps, bifurcation diagrams, and related analyses. It is shown that in the case of a 5D extension, we have obtained chaotic trajectories; meanwhile the 6D extension shows quasiperiodic and hyperchaotic behaviors and it exhibits strange nonchaotic attractor (SNA) features.

KW - Lü model

KW - complex variable

KW - hyperchaotic systems

KW - lyapunov exponents

KW - stability

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JF - International Journal of Nonlinear Sciences and Numerical Simulation

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Dynamic Analysis of a Lü Model in Six Dimensions and Its Projections

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Keywords

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