Chaos in Josephson junction circuits with voltage-dependent supercurrent

The system under consideration is the Josephson junction circuit model with the supercurrent depending on the voltage. All terms other than the supercurrent are treated as small perturbation. It is found that the unperturbed system has heteroclinic orbits. Melnikov's method is then applied to show the possibility of transition to chaos. By evaluating the upper bounds of the integrals in the Melnikov function, we derive the necessary conditions for transition to chaos