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Path-integral approach to dynamics in a sparse random network.

Takashi Ichinomiya1

  • 1Laboratory of Nonlinear Studies and Computation, Research Institute for Electronic Science, Hokkaido University, Sapporo, Hokkaido, Japan. miya@aurora.es.hokudai.ac.jp

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
Summary

We analyzed dynamics in sparse random networks using a path-integral approach. Our findings show network dynamics closely resemble globally coupled oscillators, confirmed by Kuramoto transition simulations.

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Area of Science:

  • Statistical physics
  • Complex systems dynamics
  • Network science

Background:

  • Mean-field approximations are standard for analyzing random network dynamics.
  • Understanding emergent behaviors in large-scale networks is crucial.

Purpose of the Study:

  • To extend mean-field approximations for sparse random networks.
  • To analyze the dynamics of such networks using the path-integral approach.

Main Methods:

  • Utilized the path-integral approach to extend mean-field theory.
  • Performed numerical simulations of the Kuramoto transition in a random network.

Main Results:

  • The variable distribution in sparse networks matches that of globally coupled oscillators.

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  • Numerical simulations confirm the theoretical analysis of the Kuramoto transition.

    • Conclusions:

    • The path-integral method provides an accurate description of sparse random network dynamics.
    • Sparse random networks exhibit collective behaviors similar to globally coupled systems.