Dynamical Analysis and Microcontroller Implementation of Linear Resistor-Capacitor Shunted Josephson Junction Model

Abstract

Theoretical analysis and microcontroller implementation of linear resistive-capacitive shunted Josephson junction (LRCSJJ) model are investigated in this paper. The rate-equations describing the LRCSJJ model has two or no equilibrium points relying on the external direct current (DC). One of the equilibrium points is a stable node and the other one is a saddle node. The hysteresis loop of current-voltage characteristics increases with the increasing of the capacitance of Josephson junction (JJ). Excitable mode, limit cycle, periodic and chaotic behaviors are found in LRCSJJ model with external alternative current thanks to the two modulation parameters largest Lyapunov exponents (LLE) diagram. LRCSJJ model exhibits two different shapes of chaotic attractors by varying the modulation amplitude. Finally, the existence of chaotic behaviors is confirmed by microcontroller results obtained from the microcontroller implementation of LRCSJJ model.