Chaos control in the Josephson junction with a resonant harmonic excitation

In the present paper, the control of chaos in the Josephson junction with two different kinds of resonant harmonic excitations, namely the additive and parametric excitations, are investigated in detail. With the Melnikov method, we have obtained the regions of excitation amplitude in which heteroclinic chaos may be generated or suppressed. Meanwhile, for suppressing the heteroclinic chaos, we have determined the prereguisite relationships between parameters of the system excitation and the control excitation. The analytical results show that phase difference between the two excitations has important effect. Moreover, numerical methods show that the phase control method is feasible not only for controlling heteroclinic chaos, but also for controlling other types of chaos in nonautonomous systems. Comparing the effect of an additive harmonious excitation with that of a parametric one, we find the former one is more effective at the small resonant frequencies, while the latter one is more effective at the large ones.