Synchronization of an excited nonlinear dynamic of the Josephson junction

This work studies the non-harmonic dynamics of the RCLSJ model of the Josephson Junction shunted by a negative conductance and by a multi-periodic pulse source which shares the same frequency as the excitation current. The negative conductance is in series with the RCLSJ model of the Josephson junction which has a non-harmonic parameter and the whole is coupled to a source multi-periodic pulse in line with an inductive circuit with internal resistance. The multi-periodic pulse source is used so that the oscillations of the excitation current do not weaken over time and to compensate for the energy losses occurring during each period. The fixed points of the system are determined and are analyzed from the differential equations which govern its dynamics. The model of our study operates in DC and AC mode depending on the behavior of the frequency of the sources and the phase difference of the junction. A range of the value of the multi-periodic pulse source pulsation and the value of the negative conductance voltage are found for complete synchronization of the system in DC and AC mode in the presence or absence of the non-harmonic dynamics of the junction. A complete study of the circuit studied is done digitally to detect new bifurcations and pathways leading to chaos. The contribution of the negative conductance and the multi-periodic pulse is also analyzed.