Stability and non-standard finite difference method of the generalized Chua's circuit

Ahmed G. Radwan; K. Moaddy; Shaher M. Momani

doi:10.1016/j.camwa.2011.04.047

Stability and non-standard finite difference method of the generalized Chua's circuit

Ahmed G. Radwan, K. Moaddy, Shaher M. Momani

Physical Sciences and Engineering

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

67 Scopus citations

Abstract

In this paper, we develop a framework to obtain approximate numerical solutions of the fractional-order Chua's circuit with Memristor using a non-standard finite difference method. Chaotic response is obtained with fractional-order elements as well as integer-order elements. Stability analysis and the condition of oscillation for the integer-order system are discussed. In addition, the stability analyses for different fractional-order cases are investigated showing a great sensitivity to small order changes indicating the poles' locations inside the physical s-plane. The GrnwaldLetnikov method is used to approximate the fractional derivatives. Numerical results are presented graphically and reveal that the non-standard finite difference scheme is an effective and convenient method to solve fractional-order chaotic systems, and to validate their stability. © 2011 Elsevier Ltd. All rights reserved.

Original language	English (US)
Pages (from-to)	961-970
Number of pages	10
Journal	Computers & Mathematics with Applications
Volume	62
Issue number	3
DOIs	https://doi.org/10.1016/j.camwa.2011.04.047
State	Published - Aug 2011

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01

ASJC Scopus subject areas

Modeling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/j.camwa.2011.04.047

Cite this

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title = "Stability and non-standard finite difference method of the generalized Chua's circuit",

abstract = "In this paper, we develop a framework to obtain approximate numerical solutions of the fractional-order Chua's circuit with Memristor using a non-standard finite difference method. Chaotic response is obtained with fractional-order elements as well as integer-order elements. Stability analysis and the condition of oscillation for the integer-order system are discussed. In addition, the stability analyses for different fractional-order cases are investigated showing a great sensitivity to small order changes indicating the poles' locations inside the physical s-plane. The GrnwaldLetnikov method is used to approximate the fractional derivatives. Numerical results are presented graphically and reveal that the non-standard finite difference scheme is an effective and convenient method to solve fractional-order chaotic systems, and to validate their stability. {\textcopyright} 2011 Elsevier Ltd. All rights reserved.",

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T1 - Stability and non-standard finite difference method of the generalized Chua's circuit

AU - Radwan, Ahmed G.

AU - Moaddy, K.

AU - Momani, Shaher M.

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PY - 2011/8

Y1 - 2011/8

N2 - In this paper, we develop a framework to obtain approximate numerical solutions of the fractional-order Chua's circuit with Memristor using a non-standard finite difference method. Chaotic response is obtained with fractional-order elements as well as integer-order elements. Stability analysis and the condition of oscillation for the integer-order system are discussed. In addition, the stability analyses for different fractional-order cases are investigated showing a great sensitivity to small order changes indicating the poles' locations inside the physical s-plane. The GrnwaldLetnikov method is used to approximate the fractional derivatives. Numerical results are presented graphically and reveal that the non-standard finite difference scheme is an effective and convenient method to solve fractional-order chaotic systems, and to validate their stability. © 2011 Elsevier Ltd. All rights reserved.

AB - In this paper, we develop a framework to obtain approximate numerical solutions of the fractional-order Chua's circuit with Memristor using a non-standard finite difference method. Chaotic response is obtained with fractional-order elements as well as integer-order elements. Stability analysis and the condition of oscillation for the integer-order system are discussed. In addition, the stability analyses for different fractional-order cases are investigated showing a great sensitivity to small order changes indicating the poles' locations inside the physical s-plane. The GrnwaldLetnikov method is used to approximate the fractional derivatives. Numerical results are presented graphically and reveal that the non-standard finite difference scheme is an effective and convenient method to solve fractional-order chaotic systems, and to validate their stability. © 2011 Elsevier Ltd. All rights reserved.

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JO - Computers & Mathematics with Applications

JF - Computers & Mathematics with Applications

IS - 3

ER -

Stability and non-standard finite difference method of the generalized Chua's circuit

Abstract

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