NONLINEAR DYNAMICAL-APPROACH TO SMALL JOSEPHSON-JUNCTION LADDER ARRAYS

Abstract

We have studied the dynamic response of small Josephson junction ladder arrays consisting of N-p Square plaquettes. Throughout the study, we have stressed the application of the techniques of nonlinear dynamics to the dynamical problem of Josephson junction arrays. We have found chaotic voltage fluctuations in the I-V curves due to homoclinic chaos for N-p greater than or equal to 2 and analyzed in detail the mechanism for its creation for a single-plaquette array with asymmetric current injection. This form of chaos is found in a wide range of the parameter space and persists under perturbations of the current configuration. The hysteresis in the I-V characteristics is explained in terms of the competition between symmetric and non-symmetric attractors. The role of the symmetry in the ladder arrays and the connection to the dynamical models of symmetric torus maps are also discussed.