Strange Fractal Attractors and Optimal Chaos of Memristor–Memcapacitor via Non-local Differentials

Abstract

The multi-dimensional electronic devices are so called memory circuit elements (memristor or memcapacitor); such memory circuit elements usually rely on previous applied voltage, current, flux or charge based on memory capability with their resistance, capacitance or inductance. In view of above fact, this manuscript investigates the non-integer modeling of memristor–memcapacitor in discrete-time domain through non-singular kernels of fractal fractional differentials and integrals operators. The governing equations of memristor–memcapacitor have been developed for the sake of the dynamical characteristics of simple chaotic circuit. The fractal fractional differentials and integrals operators have been invoked for non-integer modeling of memristor–memcapacitor that can exhibit a combination of dynamical chaotic phenomena. The numerical schemes, numerical simulations, stability analysis and equilibrium points have been highlighted in detail. The comparative chaotic graphs have been discussed in three ways (i) by keeping fractal component fixed and varying fractional component distinctly, (ii) by keeping fractional component fixed and varying fractal component distinctly and (iii) by varying both fractal component and fractional component distinctly. Our results suggest that fractal-fractional model of memristor–memcapacitor retains the memory characteristics.