Large deviation exits from a running orbit in the Josephson junction

A generalization of large deviation results to the instance where the diffusion matrix is singular is used to solve the problem of exit from the region of attraction of a stable limit cycle (running orbit) in the DC-forced Josephson junction. The associated variational problem is posed and solved as an optimal control problem. It is found that the likely exit path is through the saddle equilibrium on the separatrix. This path is computed and the asymptotic exit time is calculated. The problem of relative stability of the running orbit and the stable equilibrium is thus solved.<>