First-order synchronization transition in locally coupled maps

We study several diffusively coupled chaotic maps on periodic d -dimensional square lattices. Even and odd sublattices are updated alternately, introducing an effective delay. As the coupling strength is increased, the system undergoes a first-order phase transition from a multistable to a synchronized phase. At the transition point, the largest Lyapunov exponent of the system changes sign contrary to the earlier studies which predicted the same to be negative. Further increase in coupling strength shows desynchronization where the phase space splits into two ergodic regions. We argue that the nature of desynchronization transition strongly depends on the differentiability of the maps.