Control of the chaotic dynamics of the RCLSJ model of the Josephson junction by the frequency of an excitation current and the internal resistance of a coil

Abstract In this paper, we controlled the chaotic dynamics of the RCLSJ model of the Josephson junction by the frequency of an excitation current and the internal resistance of an coil. We have used an alternating current source and the internal resistance of the coil of the inductive circuit is considered. The assembly is coupled to a shunted inductive junction (RCLSJ) model where the non-harmonic dynamics of the model is taken into account. The fixed points of the system are determined and are analyzed from the differential equations which govern its dynamics. The numerical results showed that the model studied can be used in direct and alternating conditions depending on the value of the frequency of the excitation current and the phase difference of the junction. In continuous mode, the model exhibits chaotic behavior at the beginning and is regular thereafter. This initial chaotic behavior has become regular due to the internal resistance of the coil. In the alternative regime, the model presents more complex dynamic behaviors. The system behaves like a current adapter depending on the frequency and phase difference conditions of the junction. Comprehensive study of the system reveals many new forks and pathways leading to chaos that have been verified using hardware experiments in addition to numerical calculations.