Chaotic Dynamics of a Josephson Junction with Nonlinear Damping

We study the chaotic dynamics of a Josephson junction with nonlinear damping. It is found that with the increasing dc bias the system undergoes a process from a biperiodical state to a chaotic one via a period-doubling route. Interestingly, when the value of the dc bias increases further, the number of the chaotic attractors also increases accordingly. These chaotic attractors appear one after another in different intervals and regions with time. Through a feedback controlling strategy the chaos can be effectively suppressed. We also find that the current between the two separated superconductors of the junction can increase or decrease monotonously with time in some parameter spaces.