On configuring new choatic behaviours for a variable fractional-order memristor-based circuit in terms of Mittag-Leffler kernel

Abstract

Memristors, which are inevitably dynamical and memory components, could replace capacitors in the next-generation dynamical supercomputing converters that can exhibit behavioural characteristics, such as chaos. The nonlocal and nonsingular kernel Mittag-Leffler function (MLF) in the context of Caputo is researched in a new memristor framework via variable order. The existence and uniqueness of the fractional depiction of the specific process are confirmed using the Banach fixed-point approach for the contraction criterion. A newly developed numerical scheme for fractional-order systems introduced by Toufik and Atangana is utilized to obtain the phase portraits of the suggested system for various variable-order values of the system. The memristor-based model and many chaotic patterns of the Newton–Leipnik, Rabinovich–Fabrikant, Dadras, Aizawa, Thomas’ and four-wing types were the core issues of our study. The sensitivity of the chaotic systems of the considered model will be focused with precision using the bifurcation diagrams and the Lyapunov exponent. The stability of the equilibrium points of the commensurable fractional-order chaotic system will be addressed in the context of fractional calculus. In other words, we will use the standard Matignon criterion to address the problem of stability. The main attraction and novelty of this paper will be the use of the Lyapunov exponent (LE˜)s. It is demonstrated that the attempted framework is chaotic as well as extremely responsive to modifications in the parameters and the small initial conditions.