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Synchronization of Kauffman networks.

L G Morelli1, D H Zanette

  • 1Consejo Nacional de Investigaciones Científicas y Técnicas, Centro Atómico Bariloche and Instituto Balseiro, 8400 Bariloche, Río Negro, Argentina.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
Summary

We analyzed synchronization in coupled Kauffman networks. Synchronization emerges via a transcritical bifurcation, accurately described by an annealed model for large networks.

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Area of Science:

  • Complex systems
  • Network theory
  • Nonlinear dynamics

Background:

  • Kauffman networks are models of gene regulatory networks.
  • Understanding synchronization in coupled chaotic systems is crucial for complex systems analysis.

Purpose of the Study:

  • To analyze the synchronization transition in coupled identical Kauffman networks.
  • To investigate the validity of an annealed model for describing network dynamics.
  • To explore finite-size effects and preliminary results for disordered networks.

Main Methods:

  • Analysis of synchronization transition in the chaotic phase.
  • Application of an annealed model for Kauffman networks.
  • Comparison of analytical predictions with numerical simulations.
  • Detailed study of finite-size effects.

Main Results:

  • Synchronization appears through a transcritical bifurcation.
  • The annealed model provides an approximate description of coupled network dynamics.
  • Analytical predictions align well with numerical results for large networks.
  • Finite-size effects were studied in detail.

Conclusions:

  • The transcritical bifurcation is a key mechanism for synchronization in these networks.
  • The annealed model offers a useful approximation for coupled Kauffman network dynamics.
  • Numerical and analytical findings are consistent, especially for larger systems.

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