Theoretical Analysis of Smooth Nonlinear Resistor–Capacitor Shunted Josephson Junction Circuit and Its Microcontroller-Based Digital Design with Graphic LCD

This paper reports on the theoretical analysis and microcontroller implementation of smooth nonlinear resistor–capacitor shunted Josephson junction (SNRCSJJ) circuit. The smooth nonlinear resistor is described by a cosine interference term. The stability of the equilibrium points obtained from the rate equations describing the SNRCSJJ circuit reveals the existence of saddle node and transcritical bifurcation. The hysteresis loop widths of current–voltage curves increase with the increase in the coherence parameter. Periodic behaviors, relaxation behaviors, chaotic behaviors, bistable periodic attractors, and coexisting attractors are found during the numerical analysis by varying the coherence parameter and modulation parameters of alternative current (AC). In order to use both in real engineering applications and for educational purposes, microcontroller-based digital design with graphic LCD (liquid crystal display) of the SNRCSJJ circuit is designed. The digital design results matched the simulation results.