Transition from clustered state to spatiotemporal chaos in a small-world networks.

We study the spatiotemporal patterns in coupled circle maps on a small-world network. This system shows a rich phase diagram with several interesting phases. In particular, we make a detailed study of transition from clustered phase to spatiotemporal chaos. In the clustered state, observed at smaller coupling values, some sites stay close to the fixed point forever while others explore a larger part of the phase space. For stronger coupling, there is a transition to spatiotemporal chaos where no site stays close to fixed point forever. We study this transition as a dynamic phase transition. Persistence acts as a good order parameter for this transition. We find that this transition is continuous. We also briefly discuss other phases observed in this system.