Dynamical behaviors, control and synchronization of a new chaotic model with complex variables and cubic nonlinear terms

Dynamical behaviors, control and synchronization of a new chaotic model with complex variables and cubic nonlinear terms

A novel chaotic model with complex variables and cubic non-linear terms was proposed. The new system is a six dimensional continuous real autonomous chaotic system. The characteristics of this system containing invariance, dissipation, equilibria and their stability, Lyapunov exponents, Lyapunov dim...

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Main Authors: Emad E. Mahmoud, Madeha A. Al-Adwani
Format: Article
Language:English
Published: Elsevier 2017-01-01
Series:Results in Physics
Online Access:http://www.sciencedirect.com/science/article/pii/S2211379717301766
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spelling doaj-59cef9ea8b1a4574ac9502d7cf8f3dfd2020-11-25T02:01:11ZengElsevierResults in Physics2211-37972017-01-01713461356Dynamical behaviors, control and synchronization of a new chaotic model with complex variables and cubic nonlinear termsEmad E. Mahmoud0Madeha A. Al-Adwani1Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt; Department of Mathematics, Faculty of Science, Taif University, Taif, Saudi Arabia; Corresponding author at: Department of Mathematics, Faculty of Science, Taif University, Taif, Saudi Arabia.Department of Mathematics, Faculty of Science, Taif University, Taif, Saudi ArabiaA novel chaotic model with complex variables and cubic non-linear terms was proposed. The new system is a six dimensional continuous real autonomous chaotic system. The characteristics of this system containing invariance, dissipation, equilibria and their stability, Lyapunov exponents, Lyapunov dimension, bifurcation diagrams and chaotic achievement are studied. Converting and turning the system chaotic behavior to its unstable trivial fixed point via the Lyapunov stability theorem. An approach proposed to analyze the system chaos synchronization. Analytical expressions are derived for control functions. The chaos synchronization results were employed to develop a simple application in secure communication. Numerical effects computed to experiment the control forces scientific expressions gravity and to show the chaos synchronization of a chaotic system. Keywords: Chaotic, Control, Synchronization, Lyapunov stability, Complexhttp://www.sciencedirect.com/science/article/pii/S2211379717301766
collection DOAJ
language English
format Article
sources DOAJ
author Emad E. Mahmoud
Madeha A. Al-Adwani
spellingShingle Emad E. Mahmoud
Madeha A. Al-Adwani
Dynamical behaviors, control and synchronization of a new chaotic model with complex variables and cubic nonlinear terms
Results in Physics
author_facet Emad E. Mahmoud
Madeha A. Al-Adwani
author_sort Emad E. Mahmoud
title Dynamical behaviors, control and synchronization of a new chaotic model with complex variables and cubic nonlinear terms
title_short Dynamical behaviors, control and synchronization of a new chaotic model with complex variables and cubic nonlinear terms
title_full Dynamical behaviors, control and synchronization of a new chaotic model with complex variables and cubic nonlinear terms
title_fullStr Dynamical behaviors, control and synchronization of a new chaotic model with complex variables and cubic nonlinear terms
title_full_unstemmed Dynamical behaviors, control and synchronization of a new chaotic model with complex variables and cubic nonlinear terms
title_sort dynamical behaviors, control and synchronization of a new chaotic model with complex variables and cubic nonlinear terms
publisher Elsevier
series Results in Physics
issn 2211-3797
publishDate 2017-01-01
description A novel chaotic model with complex variables and cubic non-linear terms was proposed. The new system is a six dimensional continuous real autonomous chaotic system. The characteristics of this system containing invariance, dissipation, equilibria and their stability, Lyapunov exponents, Lyapunov dimension, bifurcation diagrams and chaotic achievement are studied. Converting and turning the system chaotic behavior to its unstable trivial fixed point via the Lyapunov stability theorem. An approach proposed to analyze the system chaos synchronization. Analytical expressions are derived for control functions. The chaos synchronization results were employed to develop a simple application in secure communication. Numerical effects computed to experiment the control forces scientific expressions gravity and to show the chaos synchronization of a chaotic system. Keywords: Chaotic, Control, Synchronization, Lyapunov stability, Complex
url http://www.sciencedirect.com/science/article/pii/S2211379717301766
work_keys_str_mv AT emademahmoud dynamicalbehaviorscontrolandsynchronizationofanewchaoticmodelwithcomplexvariablesandcubicnonlinearterms
AT madehaaaladwani dynamicalbehaviorscontrolandsynchronizationofanewchaoticmodelwithcomplexvariablesandcubicnonlinearterms
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