Stability and non-standard finite difference method of the generalized Chuas circuit
In this paper, we develop a framework to obtain approximate numerical solutions of the fractional-order Chuas 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 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.
chuas circuit memristor non-standard finite difference schemes chaotic systems fractional differential equations