Fractal resistive–capacitive–inductive shunted Josephson junction: Theoretical investigation and microcontroller implementation

Abstract

The paper captures the analytical and numerical investigations of the fractal resistive–capacitive–inductive shunted Josephson junction (FRCLSJJ) and its microcontroller implementation (MCI). The rate equations of FRCLSJJ are established and based on the Routh–Hurwitz criterion, two equilibrium points are reported with one unconditionally stable and the other unstable for the direct current used for junction excitation less than or equal to one. When this current is greater than one, the FRCLSJJ exhibits no equilibrium point. The contribution of fractal parameters to the dynamics of FRCLSJJ is investigated on fast bursting, regular spiking, relaxation behaviors, and periodic bursting. The FRCLSJJ is characterized by fine dynamics such as different presentations of complex behaviors, the coexistence of periodic and chaotic hidden attractors, chaotic hidden attractors, antimonotonicity, periodic attractors, and periodic and chaotic bubble hidden attractors for varying system parameters. And in the last section of the investigation, the MCI of FRCSJJ is realized with the results establishing a qualitative agreement with numerically simulated results.