Clustering behavior of oscillator arrays

Abstract

We consider the time-periodic behavior of oscillator arrays subject to global coupling. Results are presented for experiments on an electrical circuit comprised of p-n diode junctions, as well as numerical simulations of an array of iterative maps. In the vicinity of a single-element period-doubling bifurcation, a large number of periodic attractors coexist, differing by the degree of synchronization of the array. Certain general features of the observed dynamical behavior can be understood using a combination of stability analysis, symmetry considerations, combinatorics, and relative sizes of the basins of attraction.