Dynamical probing of piecewise nonlinear resistor-capacitor inductor shunted Josephson junction circuit embedded in microcontroller implementation

Abstract

This paper evaluates the theoretical and microcontroller execution probing of piecewise nonlinear resistor-capacitor inductor shunted Josephson junction circuit (PNRCISJJC). Kirchhoff's laws establish the equivalent rate equations of the PNRCISJJC where two steady states with one stable and its counterpart unstable for excitation current less than or equal to one with a hat tip to Routh–Hurwitz criterion. No steady state for the applied current greater than one is observed in the PNRCISJJC. The PNRCISJJC exhibits bursting behaviors, varying structures of hidden chaotic characteristics, bistable period-4-oscillations, coexisting behaviors, regular and hidden chaotic bubbles, and antimonotonicity. Furthermore, linear offset boosting based on the current and voltage state variables uncovered that the polarity of the hidden chaotic signal of either state variable can be flexibly altered by varying the offset boosting parameters. The agreement between dynamical analysis and microcontroller realization dynamics finalizes the investigation.