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

Authors:
A. G. Radwan;K. Moaddy;Shaher Momani
Affiliations:
Electrical Engineering Department, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia and Department of Engineering Mathematics, Faculty of Engineering, Cairo Univers ...;School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Malaysia;Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan
Venue:
Computers & Mathematics with Applications
Year:
2011

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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 Grunwald-Letnikov 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.