In this paper, nonlinear dynamic and chaotic behaviors of Josephson system subjected to combined bounded noise and harmonic excitation are investigated. Theoretically, the stochastic Melnikov method is employed to establish the necessary conditions of existence of chaotic motion in the system. Numerical simulations, including the safe basins, the maximal Lyapunov exponent and the Poincare map, are carried out according to the necessary conditions for the system’s parameters. They show that routes of the system turn faster into random chaos as the amplitude of the stochastic noise excitation increases. Finally by using sliding mode control method, the controller is designed to eliminate the adverse effect of the noise and improve the working performance of the system.
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