Chaotic Oscillations in a Fractional-Order Circuit with a Josephson Junction Resonator and Its Synchronization Using Fuzzy Sliding Mode Control

Abstract

A linear resistive capacitive inductive shunted model of a Josephson junction with a topologically nontrivial behaviour is considered in this paper. We have considered a fractional-order flux-controlled memristor to effectively model the feedback flux effects across the Josephson junction (JJ). The mathematical model of the proposed JJ oscillator is derived, and the dimensionless model is used to study the various dynamical properties of the oscillator. The stability plot shows that the proposed oscillator has both stable and unstable regions of oscillations for different choices of equilibrium points and fractional order. The bifurcation plots are presented to understand the route to crisis, and we have also shown that the oscillator has regions of coexisting attractors. We have also achieved the synchronization of the proposed oscillator using fuzzy sliding mode control with the master and slave systems considered with different parameter sets. The chattering amplitude is estimated by using the fuzzy logic, and it is used in the synchronization algorithm to minimize the error.