Stochastic theory of synchronization transitions in extended systems

Details Stochastic theory of synchronization transitions in extended systems Stochastic theory of synchronization transitions in extended systems

2003-01-07

arxiv.org/abs/cond-mat/0301059v2

Physics

Condensed Matter

Statistical Mechanics

To appear in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.90.204101

We propose a general Langevin equation describing the universal properties of synchronization transitions in extended systems. By means of theoretical arguments and numerical simulations we show that the proposed equation exhibits, depending on parameter values, either: i) a continuous transition in the bounded Kardar-Parisi-Zhang universality class, with a zero largest Lyapunov exponent at the critical point; ii) a continuous transition in the directed percolation class, with a negative Lyapunov exponent, or iii) a discontinuous transition (that is argued to be possibly just a transient effect). Cases ii) and iii) exhibit coexistence of synchronized and unsynchronized phases in a broad (fuzzy) region. This phenomenology reproduces almost all the reported features of synchronization transitions of coupled map lattices and other models, providing a unified theoretical framework for the analysis of synchronization transitions in extended systems.

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