Emergence of long range order for sublattice update in coupled map lattices

We study coupled map lattices in which lattice is divided into k sublattices updated sequentially. We obtain stability conditions for synchronized fixed point for any coupling. For synchronous update and nonlinear coupling, synchronized fixed point cannot be stabilized. But it is possible for a sublattice update. Novel bifurcations such as bifurcation to period-3 can be obtained in this case. Thus the phenomena which are usually not observed in coupled map lattices with synchronous dynamics can be observed with a sublattice update. We define an order parameter to quantify the transition to synchronization and observe a power law decay at the critical point. We also observe a power law decay of persistence at the critical point. The exponents change with k and approach a limiting value. Graphical abstract