On a Memristor-Based Hyperchaotic Circuit in the Context of Nonlocal and Nonsingular Kernel Fractional Operator

Memristor is a nonlinear and memory element that has a future of replacing resistors for nonlinear circuit computation. It exhibits complex properties such as chaos and hyperchaos. A five-dimensional memristor-based circuit in the context of a nonlocal and nonsingular fractional derivative is consid...

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Autores principales:	Shahram Rezapour, Chernet Tuge Deressa, Sina Etemad
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/563e4290b4af4a838794ec9452be0cd0
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spelling	oai:doaj.org-article:563e4290b4af4a838794ec9452be0cd02021-11-08T02:37:04ZOn a Memristor-Based Hyperchaotic Circuit in the Context of Nonlocal and Nonsingular Kernel Fractional Operator2314-478510.1155/2021/6027246https://doaj.org/article/563e4290b4af4a838794ec9452be0cd02021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/6027246https://doaj.org/toc/2314-4785Memristor is a nonlinear and memory element that has a future of replacing resistors for nonlinear circuit computation. It exhibits complex properties such as chaos and hyperchaos. A five-dimensional memristor-based circuit in the context of a nonlocal and nonsingular fractional derivative is considered for analysis. The Banach fixed point theorem and contraction principle are utilized to verify the existence and uniqueness of the solution of the five-dimensional system. A numerical method developed by Toufik and Atangana is used to get approximate solutions of the system. Local stability analysis is examined using the Matignon fractional-order stability criteria, and it is shown that the trivial equilibrium point is unstable. The Lyapunov exponents for different fractional orders exposed that the nature of the five-dimensional fractional-order system is hyperchaotic. Bifurcation diagrams are obtained by varying the fractional order and two of the parameters in the model. It is shown using phase-space portraits and time-series orbit figures that the system is sensitive to derivative order change, parameter change, and small initial condition change. Master-slave synchronization of the hyperchaotic system was established, the error analysis was made, and the simulation results of the synchronized systems revealed a strong correlation among themselves.Shahram RezapourChernet Tuge DeressaSina EtemadHindawi LimitedarticleMathematicsQA1-939ENJournal of Mathematics, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Shahram Rezapour Chernet Tuge Deressa Sina Etemad On a Memristor-Based Hyperchaotic Circuit in the Context of Nonlocal and Nonsingular Kernel Fractional Operator
description	Memristor is a nonlinear and memory element that has a future of replacing resistors for nonlinear circuit computation. It exhibits complex properties such as chaos and hyperchaos. A five-dimensional memristor-based circuit in the context of a nonlocal and nonsingular fractional derivative is considered for analysis. The Banach fixed point theorem and contraction principle are utilized to verify the existence and uniqueness of the solution of the five-dimensional system. A numerical method developed by Toufik and Atangana is used to get approximate solutions of the system. Local stability analysis is examined using the Matignon fractional-order stability criteria, and it is shown that the trivial equilibrium point is unstable. The Lyapunov exponents for different fractional orders exposed that the nature of the five-dimensional fractional-order system is hyperchaotic. Bifurcation diagrams are obtained by varying the fractional order and two of the parameters in the model. It is shown using phase-space portraits and time-series orbit figures that the system is sensitive to derivative order change, parameter change, and small initial condition change. Master-slave synchronization of the hyperchaotic system was established, the error analysis was made, and the simulation results of the synchronized systems revealed a strong correlation among themselves.
format	article
author	Shahram Rezapour Chernet Tuge Deressa Sina Etemad
author_facet	Shahram Rezapour Chernet Tuge Deressa Sina Etemad
author_sort	Shahram Rezapour
title	On a Memristor-Based Hyperchaotic Circuit in the Context of Nonlocal and Nonsingular Kernel Fractional Operator
title_short	On a Memristor-Based Hyperchaotic Circuit in the Context of Nonlocal and Nonsingular Kernel Fractional Operator
title_full	On a Memristor-Based Hyperchaotic Circuit in the Context of Nonlocal and Nonsingular Kernel Fractional Operator
title_fullStr	On a Memristor-Based Hyperchaotic Circuit in the Context of Nonlocal and Nonsingular Kernel Fractional Operator
title_full_unstemmed	On a Memristor-Based Hyperchaotic Circuit in the Context of Nonlocal and Nonsingular Kernel Fractional Operator
title_sort	on a memristor-based hyperchaotic circuit in the context of nonlocal and nonsingular kernel fractional operator
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/563e4290b4af4a838794ec9452be0cd0
work_keys_str_mv	AT shahramrezapour onamemristorbasedhyperchaoticcircuitinthecontextofnonlocalandnonsingularkernelfractionaloperator AT chernettugederessa onamemristorbasedhyperchaoticcircuitinthecontextofnonlocalandnonsingularkernelfractionaloperator AT sinaetemad onamemristorbasedhyperchaoticcircuitinthecontextofnonlocalandnonsingularkernelfractionaloperator
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On a Memristor-Based Hyperchaotic Circuit in the Context of Nonlocal and Nonsingular Kernel Fractional Operator

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