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

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