Mathematical analysis and emulation of the fractional-order cubic flux-controlled memristor
Babajide Oluwatosin Oresanya, Gangquan Si, Zhang Guo, Xiang Xu, Yiyuan Bie
Abstract
Cubic model of flux-controlled memristor model is presented in this work and the model is analyzed at various fractional orders. Analytic computations with a sinusoidal source shows that the v-i loop can have up to two more additional intersection points aside from the origin and are located in the 1st and 3rd quadrants respectively. The locations of the intersection points and the area of the v-i loops are both dependent on the excitation signal frequency and fractional orders. Floating and Grounded emulator circuits for the cubic models are designed incorporating a fractional order integrator designed from the 2nd-order rational approximation of s-α. PSPICE simulations verify the correctness of the numerical analysis and calculations. An application example shows that the fractional-order cubic model can generate chaos in Chua’s circuit and produced an increase in the system dynamics.