Nonlinear dynamics of a Josephson junction coupled to a diode and a negative conductance

We studied the nonlinear dynamics of a shunted inductive Josephson junction coupled to a diode and a negative conductance. Taking into account the non-harmonicity of the junction, based on Kirchhoff's laws, we have developed the mathematical model which governs the dynamics of the circuit. The fixed points of the system are determined, and their stabilities are analyzed using the Routh-Hurwitz criterion. The bifurcation and transition to chaos of the model are studied using the the fourth-order Runge-Kutta method; the system displays a rich dynamics. The range of values of each parameter leading to periodic and chaotic electrical oscillations is obtained through the analysis of the effect of these parameters on each type of dynamics. Finally, the implementation by microcontroller is carried out in order to experimentally verify the different dynamics obtained numerically.