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. © 2011 Elsevier Ltd. All rights reserved.

Citation
Radwan, A. G., Moaddy, K., & Momani, S. (2011). Stability and non-standard finite difference method of the generalized Chua’s circuit. Computers & Mathematics with Applications, 62(3), 961–970. doi:10.1016/j.camwa.2011.04.047

Publisher
Elsevier BV

Journal
Computers & Mathematics with Applications

DOI
10.1016/j.camwa.2011.04.047

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