Suppressing Chaos in Josephson Junction Model with Coexisting Attractors and Investigating Its Collective Behavior in a Network

The controls of chaotic and coexisting attractors and collective dynamics in linear resistive-capacitive-inductive shunted Josephson junction (LRCISJJ) model are investigated in this paper. A single feedback controller is designed to control chaos found in the LRCISJJ model. Analytical calculations and numerical simulations are carried out to show the serviceableness of the designed single controller. In addition, the coexistence between chaotic and limit cycle attractors is ruined and controlled to a desired trajectory by using the linear augmentation control method. Finally, since the LRCISJJ shows spiking and bursting behaviors, a 2D lattice array of the LRCISJJ model is constructed in order to understand its network behavior. The spiral wave formation in the network is studied in the presence of heterogeneity. To further confirm the excitability heterogeneity in the network, the periods of each node are used to show the periodicity pattern in the network.