Controlling Chaos in Josephson-Junction Using Nonlinear Backstepping Controller

In this paper, a nonlinear backstepping controller has been designed to control bifurcation as well as incipient chaos that has been experienced in the RCLSJ (shunted nonlinear resistive-capacitive-inductance) Josephson-Junction. The results show that the system, without controller, has a dangerous Hopf bifurcation point that lead to chaotic behavior. For certain values of the external direct current (I₀), the system becomes chaotic. On the other hand, the nonlinear backstepping controller converts the chaotic region into a stable periodic solution region