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We developed a new analytical method to study how complex networks switch between states due to internal noise. This technique quantifies fluctuation probabilities and switching times, offering insights into network behavior and targeted interventions.

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Area of Science:

  • Complex systems analysis
  • Network science
  • Statistical physics

Background:

  • Complex networks exhibit emergent behaviors and can transition between different states.
  • Internal noise is a key factor driving state switching in these systems.
  • Understanding large fluctuations is crucial for predicting network dynamics.

Purpose of the Study:

  • To develop an analytical technique for studying large fluctuations and state switching in complex networks driven by internal noise.
  • To analyze the most probable path of fluctuations between ordered states.
  • To quantify the influence of network heterogeneity on fluctuation probabilities and switching times.

Main Methods:

  • Analytical technique based on order-disorder kinetics.
  • Construction and analysis of optimal fluctuation paths.
  • Computation of large fluctuation distributions and switching time scales.
  • Quantification of network heterogeneity effects using eigenvector participation ratio.

Main Results:

  • The method computes fluctuation distributions and switching time scales for networks under mean-field assumptions.
  • Network heterogeneity was found to influence scaling patterns and fluctuation probabilities.
  • Probability of large fluctuations near transitions decreases exponentially with the network's participation ratio.

Conclusions:

  • The proposed analytical technique provides a framework for understanding and predicting state switching in complex networks.
  • Network structure, particularly heterogeneity, significantly impacts fluctuation dynamics.
  • The theory offers guidance on how to target networks to optimize switching times.