A simple technique for studying chaos using jerk equation with discrete time sine map

Muhammad Haseeb Arshad; Mahmoud Kassas; Alaa E. Hussein; Mohammad A. Abido

doi:10.3390/app11010437

A simple technique for studying chaos using jerk equation with discrete time sine map

Muhammad Haseeb Arshad, Mahmoud Kassas, Alaa E. Hussein^*, Mohammad A. Abido

^*Corresponding author for this work

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

8 Scopus citations

Abstract

Over the past decade, chaotic systems have found their immense application in different fields, which has led to various generalized, novel, and modified chaotic systems. In this paper, the general jerk equation is combined with a scaled sine map, which has been approximated in terms of a polynomial using Taylor series expansion for exhibiting chaotic behavior. The paper is based on numerical simulation and experimental verification of the system with four control parameters. The proposed system’s chaotic behavior is verified by calculating different chaotic invariants using MATLAB, such as bifurcation diagram, 2-D attractor, Fourier spectra, correlation dimension, and Maximum Lyapunov Exponent (MLE). Experimental verification of the system was carried out using Op-Amps with analog multipliers.

Original language	English
Article number	437
Pages (from-to)	1-16
Number of pages	16
Journal	Applied Sciences (Switzerland)
Volume	11
Issue number	1
DOIs	https://doi.org/10.3390/app11010437
State	Published - 1 Jan 2021

Bibliographical note

Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

Keywords

Bifurcation
Chaos
Correlation dimension
Jerk equation
Lyapunov exponent
Poincare section
Sine map

ASJC Scopus subject areas

General Materials Science
Instrumentation
General Engineering
Process Chemistry and Technology
Computer Science Applications
Fluid Flow and Transfer Processes

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10.3390/app11010437

Cite this

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title = "A simple technique for studying chaos using jerk equation with discrete time sine map",

abstract = "Over the past decade, chaotic systems have found their immense application in different fields, which has led to various generalized, novel, and modified chaotic systems. In this paper, the general jerk equation is combined with a scaled sine map, which has been approximated in terms of a polynomial using Taylor series expansion for exhibiting chaotic behavior. The paper is based on numerical simulation and experimental verification of the system with four control parameters. The proposed system{\textquoteright}s chaotic behavior is verified by calculating different chaotic invariants using MATLAB, such as bifurcation diagram, 2-D attractor, Fourier spectra, correlation dimension, and Maximum Lyapunov Exponent (MLE). Experimental verification of the system was carried out using Op-Amps with analog multipliers.",

keywords = "Bifurcation, Chaos, Correlation dimension, Jerk equation, Lyapunov exponent, Poincare section, Sine map",

author = "Arshad, \{Muhammad Haseeb\} and Mahmoud Kassas and Hussein, \{Alaa E.\} and Abido, \{Mohammad A.\}",

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AU - Arshad, Muhammad Haseeb

AU - Kassas, Mahmoud

AU - Hussein, Alaa E.

AU - Abido, Mohammad A.

PY - 2021/1/1

Y1 - 2021/1/1

N2 - Over the past decade, chaotic systems have found their immense application in different fields, which has led to various generalized, novel, and modified chaotic systems. In this paper, the general jerk equation is combined with a scaled sine map, which has been approximated in terms of a polynomial using Taylor series expansion for exhibiting chaotic behavior. The paper is based on numerical simulation and experimental verification of the system with four control parameters. The proposed system’s chaotic behavior is verified by calculating different chaotic invariants using MATLAB, such as bifurcation diagram, 2-D attractor, Fourier spectra, correlation dimension, and Maximum Lyapunov Exponent (MLE). Experimental verification of the system was carried out using Op-Amps with analog multipliers.

AB - Over the past decade, chaotic systems have found their immense application in different fields, which has led to various generalized, novel, and modified chaotic systems. In this paper, the general jerk equation is combined with a scaled sine map, which has been approximated in terms of a polynomial using Taylor series expansion for exhibiting chaotic behavior. The paper is based on numerical simulation and experimental verification of the system with four control parameters. The proposed system’s chaotic behavior is verified by calculating different chaotic invariants using MATLAB, such as bifurcation diagram, 2-D attractor, Fourier spectra, correlation dimension, and Maximum Lyapunov Exponent (MLE). Experimental verification of the system was carried out using Op-Amps with analog multipliers.

KW - Bifurcation

KW - Chaos

KW - Correlation dimension

KW - Jerk equation

KW - Lyapunov exponent

KW - Poincare section

KW - Sine map

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DO - 10.3390/app11010437

M3 - Article

AN - SCOPUS:85099911892

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JO - Applied Sciences (Switzerland)

JF - Applied Sciences (Switzerland)

IS - 1

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ER -

A simple technique for studying chaos using jerk equation with discrete time sine map

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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