Melnikov's method for nonperiodic perturbations and the bifurcations in a Josephson junction

We consider a Josephson junction with an applied dc current and nonperiodic time-dependent magnetic field. Despite this nonperiodicity, one may use Melnikov's method to derive the bifurcation curves analytically. We give the critical theoretical value I/sub c/ of the dc current separating qualitatively different regions, essentially one region where the solutions (Josephson phase difference phi) rotate (infinite period) and another region where they oscillate (finite period). Numerical simulations are given and the results are in good agreement with the theoretical predictions