2002/12/18 by F. Ginelli, Francesco Ginelli, R. Livi +5 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.67.046217
published as Phys. Rev E 67 (2003) 046217
arxiv created 2002/12/18 · openalex publication_date 2003/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the nature of the synchronization transition in spatially extended systems by discussing a simple stochastic model. An analytic argument is put forward showing that, in the limit of discontinuous processes, the transition belongs to the directed percolation (DP) universality class. The analysis is complemented by a detailed investigation of the dependence of the first passage time for the amplitude of the difference field on the adopted threshold. We find the existence of a critical threshold separating the regime controlled by linear mechanisms from that controlled by collective phenomena. As a result of this analysis, we conclude that the synchronization transition belongs to the DP class also in continuous models. The conclusions are supported by numerical checks on coupled map lattices too.