Relationship between directed percolation and the synchronization transition in spatially extended systems

F Ginelli, R Livi, A Politi, A Torcini

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19 Citations (Scopus)


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.

Original languageEnglish
Article number046217
Number of pages10
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number4
Publication statusPublished - 25 Apr 2003


  • density series expansions
  • phase-transitions
  • absorbing states
  • noise
  • chaos
  • behavior
  • models
  • square

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