Dynamical Probing and Microcontroller Implementation of a Josephson Junction Circuit With 2π− and 4π−Periodic Supercurrent Components

Abstract

Abstract This paper is aimed at establishing the theoretical study and microcontroller validation of the resistive–capacitive shunted Josephson junction (JJ) circuit with 2π− and 4π−periodic superconducting current components (RCSJJ2-4PSCC). According to the Routh–Hurwitz criteria, the rate equations for the RCSJJ2-4PSCC exhibit different behaviors based on operating conditions. When the system operates strictly in the 2π− or 4π−periodic regime, it may have either no equilibrium points or two equilibrium points, which are a stable-node and a saddle-node, influenced by the excitation current. In contrast, when the RCSJJ2-4PSCC functions under conditions where both the 2π− and 4π−periodic regimes coexist, it displays no equilibrium points, or two, four, or even eight equilibrium points. The stability of these points varies, particularly with the emergence of a pitchfork bifurcation based on the fractional parameter and stimulation current source. The hysteresis loop is sensitive to variation of the fractional parameter of the RCSJJ2-4PSCC. The RCSJJ2-4PSCC reveals various behaviors, including regular, period-doubling, bistable regular, bistable chaotic, and chaotic characteristics, as well as the coexistence of these states. These dynamical attractors show qualitative agreement with the results from the microcontroller implementation. By introducing via addition, a boosting parameter to the voltage, the orientations of the chaotic signals are adjusted dynamically by altering the boosting parameter.