Heteroclinic chaos in a Josephson-junction system perturbed by dichotomous noise excitation

The chaotic behavior in a Josephson-junction system perturbed by dichotomous noise excitation is discussed in detail. Conditions for the onsets of chaos are derived by virtue of the random Melnikov method together with the mean-square criterion. It is shown that with the increase of the noise transition rate, the threshold of the dichotomous noise amplitude for the onset of chaos in the system increases. The effects of dichotomous noise on the Josephson-junction system are also determined by numerical simulations via the mean largest Lyapunov exponents, which verifies that the injection of the dichotomous noise can cause the change of the sign of the largest Lyapunov exponent and lead to noise-induced chaos. Phase portraits and time histories are further used to verify these results. It can be concluded that by changing the internal parameters of the dichotomous noise, we can adjust the threshold for the onset of the chaos and then control dynamical behaviors in the Josephson-junction system subjected to dichotomous noise excitation