Numerical study of a nonlinear fractional chaotic Chua's circuit

Nehad Ali Shah; Iftikhar Ahmed; Kanayo K. Asogwa; Azhar Ali Zafar; Wajaree Weera; Ali Akgül; Nehad Ali Shah; Iftikhar Ahmed; Kanayo K. Asogwa; Azhar Ali Zafar; Wajaree Weera; Ali Akgül

doi:10.3934/math.2023083

AIMS Mathematics

2023, Volume 8, Issue 1: 1636-1655. doi: 10.3934/math.2023083

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Research article

Numerical study of a nonlinear fractional chaotic Chua's circuit

1.
Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea
2.
Department of Mathematics & Statistics, University of Swat, Khyber Pukhtoonkhwa, Pakistan
3.
Department of Mathematics, Nigeria Maritime University, Okerenkoko, Delta State, Nigeria
4.
Department of Mathematics, GC University Lahore, Lahore, Pakistan
5.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand
6.
Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt Turkey
7.
Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, PC: 99138, Nicosia /Mersin 10-Turkey

Received: 24 July 2022 Revised: 08 October 2022 Accepted: 13 October 2022 Published: 24 October 2022
MSC : 35R11, 35K23

As an exponentially growing sensitivity to modest perturbations, chaos is pervasive in nature. Chaos is expected to provide a variety of functional purposes in both technological and biological systems. This work applies the time-fractional Caputo and Caputo-Fabrizio fractional derivatives to the Chua type nonlinear chaotic systems. A numerical analysis of the mathematical models is used to compare the chaotic behavior of systems with differential operators of integer order versus systems with fractional differential operators. Even though the chaotic behavior of the classical Chua's circuit has been extensively investigated, our generalization can highlight new aspects of system behavior and the effects of memory on the evolution of the chaotic generalized circuit.
- Chaos,
- nonlinear chaotic systems,
- Caputo and Caputo-Fabrizio fractional derivatives,
- chaotic generalized circuit
Citation: Nehad Ali Shah, Iftikhar Ahmed, Kanayo K. Asogwa, Azhar Ali Zafar, Wajaree Weera, Ali Akgül. Numerical study of a nonlinear fractional chaotic Chua's circuit[J]. AIMS Mathematics, 2023, 8(1): 1636-1655. doi: 10.3934/math.2023083

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Abstract

As an exponentially growing sensitivity to modest perturbations, chaos is pervasive in nature. Chaos is expected to provide a variety of functional purposes in both technological and biological systems. This work applies the time-fractional Caputo and Caputo-Fabrizio fractional derivatives to the Chua type nonlinear chaotic systems. A numerical analysis of the mathematical models is used to compare the chaotic behavior of systems with differential operators of integer order versus systems with fractional differential operators. Even though the chaotic behavior of the classical Chua's circuit has been extensively investigated, our generalization can highlight new aspects of system behavior and the effects of memory on the evolution of the chaotic generalized circuit.

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