Chaotic Dynamics of a Periodically Modulated Josephson Junction

We study the chaotic dynamics of a periodically modulated Josephson junction with damping. The general solution of the first-order perturbed equation is constructed by using the direct perturbation technique. It is theoretically found that the boundedness conditions of the general solution contain the
Melnikov chaotic criterion. When the perturbation conditions cannot be satisfied, numerical simulations demonstrate that the system can step into chaos through a period doubling route with the increase of the amplitude of the modulating term. Regulating specific parameters can effectively suppress the chaos.