We consider a simple model of the flux in a rf superconducting quantum-interference device (SQUID) ring subjected to an external periodic magnetic field. The dynamic equation describing the flux response of the SQUID is solved analytically in the absence of damping and external driving terms. We then introduce these terms as small perturbations, and construct, for this system, the Melnikov function, the zeros of which indicate the onset of homoclinic behavior. For the parameter values under consideration, excellent agreement is obtained between our theoretical predictions and numerical calculations of the stable and unstable (i.e., time-reversed) solution manifolds. A chaotic attractor is shown to appear somewhat above the homoclinic threshold.

• Received 30 November 1987

DOI:https://doi.org/10.1103/PhysRevA.37.3541