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Turbulence in small-world networks.

M G Cosenza1, K Tucci

  • 1Centro de Astrofísica Teórica, Universidad de Los Andes, Apartado Postal 26, La Hechicera, Mérida 5251, Venezuela. mcosenza@ciens.ula.ve

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 23, 2002
PubMed
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This study explores turbulence transition in small-world networks using coupled maps. It reveals how network rewiring alters the transition from second-order to first-order, offering insights into disordered systems.

Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Network science

Background:

  • Spatiotemporal intermittency is a key phenomenon in nonlinear systems.
  • Coupled map lattices are used to model complex spatiotemporal behavior.
  • Small-world networks introduce unique structural properties not found in ordered lattices.

Purpose of the Study:

  • Investigate the transition to turbulence in coupled map lattices on small-world networks.
  • Analyze the impact of network rewiring probability and coupling strength on system dynamics.
  • Characterize the order of the phase transition and identify novel collective behaviors.

Main Methods:

  • Utilized the Chaté-Manneville minimal map for local dynamics.
  • Calculated the critical boundary between laminar and turbulent regimes in the system's parameter space.

Related Experiment Videos

  • Examined the order parameter to identify changes in the phase transition and collective behavior.

    • Main Results:

    • Identified windows of relaminarization within specific parameter regions.
    • Observed a transition from second-order to first-order phase transition as rewiring probability changes.
    • Discovered a linear relationship governing the change in the order of the phase transition.
    • Found nontrivial collective behavior in the order parameter for certain parameter values.

    Conclusions:

    • Small-world network topology significantly alters turbulence transition dynamics.
    • The rewiring probability acts as a critical parameter controlling the nature of the phase transition.
    • These findings provide a framework for modeling processes in disordered, nonuniform media.