Chaotic dynamics of Josephson equation driven by constant dc and ac forcings

The chaotic dynamics of a Josephson equation driven by constant dc and ac current forcing with a shifted phase is investigated. We at first study whether there exist multiple saddle points with nontransverse homoclinic or heteroclinic orbits for unperturbed equation. Secondly, we obtain threshold for the existence of chaos by using Melnikovʹs method, and the threshold is influenced by the shifted phase. Finally some numerical results are reported in order to prove theoretical predictions.