Bifurcations of periodic solutions and chaos in Josephson system

The Josephson equation is investigated in detail: the existence and bifurca tions for harmonic and subharmonic solutions under small perturbations are obtained by using second-order averaging method and subharmonic Melnikov fu nction, and the criterion of existence for chaos is proved by Melnikov anal ysis; the bifurcation curves about n-subharmonic and heteroclinic orbits an d the driving frequency omega effects to the forms of chaotic behaviors are given by numerical simulations.