Dynamical analysis and microcontroller implementation of fractal resistive-capacitive shunted Josephson junction

Abstract

Abstract The resistive-capacitive shunted Josephson junction (JJ) with fractal propertiesis scrutinized in this paper. The rate equations betelling the fractal resistive-capacitive shunted Josephson junction (FRCSJJ) are established and have for the external biasing direct current (DC) source less than or equal to 1 two equilibrium points and no equilibrium point for the external biasing DC source greater than 1. Stability characterization by the Routh-Hurwitz critic indicates one stable equilibrium point called the ‘stable node’ and the other unstable referred to as the ‘saddle-node’. Current-voltage (C-V) characteristics depict the sensitivity of the hysteresis loop to the two fractal parameters. With an external alternative current (AC) source used in biasing FRCSJJ, the model exhibits periodic bursting oscillations, periodic oscillations, reverse period-doubling route to chaotic oscillations, periodic and chaotic bubbles, antimonotonicity, different shapes of chaotic dynamics, and mutual interaction between complex oscillations and period-4-oscillations. Finally, the accomplishment of the microcontroller implementation of FRCSJJ establishes the quantitative agreement with numerically obtained dynamics.