Phase synchronization of Wien bridge oscillator-based Josephson junction connected by hybrid synapse

In this paper, a nonlinear Josephson junction (JJ) based-Wien bridge circuit is analyzed and coupled in order to obtain synchronization through passive components. The electrical equations governing the operation of our circuit are obtained using the laws of electrical circuit analysis. Chaotic phenomenon is demonstrated in the proposed circuit using relevant indicators such as the phase portraits, bifurcation and the corresponding Lyapunov diagram. Several coupling topologies are considered to achieve the phase synchronization that provides a better understanding of the distribution of energy in the overall system. Additionally, the effect of the noise is considered which considerably brings an added value to the dynamic of the phase synchronization between oscillators. Full synchronization is observed when the resistor is connected in parallel with the inductor or capacitor while different results are obtained when the resistor is connected in series with the capacitor or inductor. Finally, fine-tuning and selection of coupling coefficients reflects a migration toward synchronization between two Josephson junction based-Wien circuits that imply the self-adaptation of the synapse when two types of synapses are active simultaneously.