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Related Experiment Videos

Dynamical properties of the synchronization transition.

Michel Droz1, Adam Lipowski

  • 1Department of Physics, University of Geneva, CH 1211 Geneva 4, Switzerland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 6, 2003
PubMed
Summary

Spreading dynamics reveals synchronization transition (ST) in coupled map lattices (CMLs). While some states align with directed percolation (DP), others exhibit unique behaviors, suggesting models with infinite absorbing states.

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Area of Science:

  • Complex systems
  • Statistical physics
  • Nonlinear dynamics

Background:

  • Synchronization transitions (ST) in one-dimensional coupled map lattices (CMLs) are crucial for understanding complex system dynamics.
  • Previous research suggested ST in discontinuous CMLs belongs to the directed percolation (DP) universality class.

Purpose of the Study:

  • To investigate ST in CMLs using spreading dynamics.
  • To analyze the universality classes of ST for different CMLs, including Bernoulli, tent, and asymmetric tent maps.
  • To compare spreading exponents with established universality classes like DP and bounded Kardar-Parisi-Zhang (BKPZ).

Main Methods:

  • Employing spreading dynamics to analyze synchronization transitions.
  • Conducting numerical simulations for Bernoulli and tent maps.

Related Experiment Videos

  • Calculating spreading exponents for various synchronized states (random and homogeneous).
  • Examining the effect of asymmetry in the tent map.

    • Main Results:

    • Spreading dynamics confirms DP universality for random synchronized states in some CMLs.
    • Homogeneous synchronized states show different exponents than DP, but their sum matches DP, indicating models with infinite absorbing states.
    • For the tent map, ST belongs to the BKPZ universality class.
    • Spreading exponents for random synchronized states of the tent map are consistent with hyperscaling, unlike homogeneous states.
    • Asymmetric tent maps exhibit BKPZ behavior for small asymmetry, transitioning to DP-like critical behavior for large asymmetry.

    Conclusions:

    • Spreading dynamics provides insights into the universality of ST in CMLs.
    • The behavior of synchronized states (random vs. homogeneous) significantly impacts the observed universality class.
    • The study highlights the rich critical phenomena in CMLs, with transitions between different universality classes depending on system parameters.