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We study a family of diffusively coupled chaotic maps on periodicd-dimensional square lattices. Even and odd sub-lattices are updatedalternately, introducing an effective delay. As the coupling strength isincreased, the system undergoes a first order phase transition from amulti-stable to a synchronized phase. Further increase in coupling strengthshows de-synchronization where the phase space splits into two ergodic regions.We argue that the de-synchronization transition is discontinuous for piece-wiselinear maps, and is continuous for non-linear maps which are differentiable.Comment: 4 pages, revtex, 4 eps figure

First-order synchronization transition in locally coupled maps