Nonlinear pattern dynamics in Josephson-junction arrays

The dynamics of a two-dimensional array of Josephson junctions under an external load is shown to be equivalent to that of a one-dimensional nonlinear chain of nonidentical, globally, and nonuniformly coupled oscillators. This allows us to determine the dynamical states and collective spatiotemporal patterns the array exhibits in response to varying initial conditions, input patterns, coupling strengths, and bias current. When the bias current goes through critical values, successive bifurcations activate spatially distinct, coupled oscillatory compartments in the array, where semirotating, whirling, and quasiperiodic and aperiodic states coexist, and induce staircase current-voltage characteristics. Classical and vortex-induced row switching phenomena, stable families of frequency synchronized and phase-locked states, subharmonics in compartment couplings, stochastic jumps, and hysteresis loops are deduced, and sequences of input patterns are Shown to be dynamically storable in the array's attractors. The dynamical formation of oscillatory compartments is also a general feature of three-dimensional Josephson-junction networks. Coherent microwave radiation emission is possible only for specific input patterns or by using symmetry-breaking array architectures. The theoretical predictions are in close agreement with the dynamics recently observed in low-temperature scanning electron microscopy experiments.