Relationship between directed percolation and the synchronization transition in spatially extended systems
Year: 2003
Authors: Ginelli F., Livi R., Politi A., Torcini A.
Autors Affiliation: Istituto Nazionale di Ottica Applicata, Largo E. Fermi 6, 50125 Firenze, Italy;
Dipartimento di Fisica, Università di Firenze, Via G. Sansone 1, 50019, Sesto Fiorentino (FI), Italy;
Istituto Nazionale di Fisica della Materia, Unità di Firenze, Via G. Sansone 1, 50019, Sesto Fiorentino (FI), Italy
Abstract: 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.
Journal/Review: PHYSICAL REVIEW E
Volume: 67 (4) Pages from: 046217-1 to: 046217-10
KeyWords: DENSITY SERIES EXPANSIONS; PHASE-TRANSITIONS; ABSORBING STATES; NOISE; CHAOSDOI: 10.1103/PhysRevE.67.046217Citations: 25data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-04-28References taken from IsiWeb of Knowledge: (subscribers only)Connecting to view paper tab on IsiWeb: Click hereConnecting to view citations from IsiWeb: Click here