SYNCHRONIZATION IN COUPLED SINE CIRCLE MAPS

We study the spatially synchronized and temporally periodic solutions of a one-dimensional lattice of coupled sine circle maps. We carry out an analytic stability analysis of this spatially synchronized and tem porally periodic case and obtain the stability matrix in a neat block diagonal form. We find spatially synchronized behavior over a substant ial range of parameter space. We have also extended the analysis to hi gher spatial periods with similar results. Numerical simulations for v arious temporal periods of the synchronized solution reveal that the e ntire structure of the Arnold tongues and the devil's staircase seen i n the case of the single circle map can also be observed for the synch ronized coupled sine circle map lattice. Our formalism should be usefu l in the study of spatially periodic behavior in other coupled map lat tices.