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

作者：Radwan A G^*; Moaddy K; Momani Shaher

来源：Computers & Mathematics with Applications, 2011, 62(3): 961-970.

DOI：10.1016/j.camwa.2011.04.047

• Fractional differential equations
• Non-standard finite difference schemes
• Fractional differential equations
• Chaotic systems
• Chua's circuit
• Memristor

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.

• 出版日期2011-8