Synchronization and Chaotic Dynamics of A Josephson Junction Shunted by A Negative Conductance

This paper presents a theoretical and numerical investigation of the RCLSJ model ‎‎(Resistively, Capacitively, and Inductively Shunted Junction), which is described by a ‎nonlinear current source characterized by the current-phase relationship ‎I_O (sin∅-α_1 sin2∅+α_2 sin3∅), coupled with a negative conductance. The rate ‎equations governing the RCLSJ model reveal that, depending on the parameter ‎regions, the system may either lack fixed points entirely or possess two or four fixed ‎points. These regions are determined by the intensity of the negative conductance ‎and the second-order harmonic term, under the assumption of a normalized critical ‎current. Our analysis demonstrates that the presence of negative conductance ‎suppresses certain hidden dynamical orders associated with periodic instabilities. ‎Furthermore, the introduction of the third-order harmonic term significantly alters ‎the nonlinear dynamics of the RCLSJ system. In addition, master-slave ‎synchronization studies indicate that the third-order harmonic modifies ‎synchronization frequencies by generating new resonance modes. For specific ‎threshold values of α2, it enhances synchronization, while variations in the intensity ‎of the negative conductance lead to higher-frequency oscillations. These different ‎influences induced by the negative conductance and the third-order harmonic term ‎of the junction suggest that the system could be used in the superconducting ‎circuits for qubits, synchronized oscillators for the generation of THz signals, and ‎also in computational neuroscience.