First-order Synchronization Transition in Locally Coupled Maps

Details First-order Synchronization Transition in Locally Coupled Maps First-order Synchronization Transition in Locally Coupled Maps

2004-02-10

arxiv.org/abs/cond-mat/0402283v1

Phys. Rev. E 70, 045202(R) (2004)

Physics

Condensed Matter

Statistical Mechanics

4 pages, revtex, 4 eps figures

Scientific paper

10.1103/PhysRevE.70.045202

We study a family of diffusively coupled chaotic maps on periodic d-dimensional square lattices. Even and odd sub-lattices are updated alternately, introducing an effective delay. As the coupling strength is increased, the system undergoes a first order phase transition from a multi-stable to a synchronized phase. Further increase in coupling strength shows de-synchronization where the phase space splits into two ergodic regions. We argue that the de-synchronization transition is discontinuous for piece-wise linear maps, and is continuous for non-linear maps which are differentiable.

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