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Relationship between directed percolation and the synchronization transition in spatially extended systems
1Istituto Nazionale di Ottica Applicata, Largo E Fermi 6, I-50125 Firenze, Italy.
Summary
This study reveals that synchronization transitions in extended systems belong to the directed percolation (DP) universality class. This finding holds for both discontinuous and continuous models, supported by analytic arguments and numerical simulations.
Area of Science:
- Complex systems
- Statistical physics
- Nonlinear dynamics
Background:
- Synchronization phenomena are crucial in spatially extended systems.
- Understanding the universality class of synchronization transitions is key to predicting system behavior.
- Previous studies often focused on specific models, lacking a unified framework.
Purpose of the Study:
- To investigate the universality class of the synchronization transition in spatially extended systems.
- To analytically demonstrate the transition's belonging to the directed percolation (DP) universality class.
- To explore the role of thresholds and collective phenomena in continuous models.
Main Methods:
- Analysis of a simple stochastic model for synchronization.
- Development of an analytic argument for the directed percolation (DP) universality class.
- Investigation of first passage time dependence on thresholds.
- Numerical simulations on coupled map lattices.
Main Results:
- The synchronization transition in discontinuous processes belongs to the directed percolation (DP) universality class.
- A critical threshold was identified, separating linear and collective regimes.
- The DP universality class holds for continuous models as well.
Conclusions:
- The synchronization transition in spatially extended systems universally belongs to the directed percolation (DP) class.
- The identified critical threshold is a key factor in understanding the transition dynamics.
- Findings are robust across different model types, including continuous ones.