2003/01/31 by Miguel A. Muñoz, Miguel A. Munoz, Romualdo Pastor‐Satorras +1 · 1 citation
Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Theoretical and Computational Physics #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physrevlett.90.204101
To appear in Phys. Rev. Lett
arxiv created 2003/04/21 · openalex publication_date 2003/05/19 · arxiv updated 2009/11/30 · openalex created_date 2020/05/13 · openalex updated_date 2026/08/04
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: (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 reproduces almost all of the reported features of synchronization transitions, providing a unified theoretical framework for the analysis of synchronization transitions in extended systems.