Synchronization in coupled sine circle maps

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Abstract
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 temporally periodic case and obtain the stability matrix in a neat block diagonal form. We find spatially synchronized behavior over a substantial range of parameter space. We have also extended the analysis to higher spatial periods with similar results. Numerical simulations for various temporal periods of the synchronized solution reveal that the entire structure of the Arnold tongues and the devil's staircase seen in the case of the single circle map can also be observed for the synchronized coupled sine circle map lattice. Our formalism should be useful in the study of spatially periodic behavior in other coupled map lattices.
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