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Area of Science:

  • Complex network theory
  • Nonlinear dynamics
  • Statistical physics

Background:

  • Directed complex networks exhibit unique transport phenomena.
  • Generalized gravity interaction models flux based on neighbor node properties.

Purpose of the Study:

  • To investigate a novel phase transition in nonlinear transport on directed complex networks.
  • To analyze the factors influencing this transition, particularly network topology.

Main Methods:

  • Analysis of nonlinear transport using the generalized gravity interaction model.
  • Analytical consideration of phase transitions for specific network configurations.
  • Comparison of the diffusion phase with real-world business firm data.

Main Results:

  • A novel phase transition between diffusion and localization phases was identified.
  • The transition point is dependent on network topology.
  • The diffusion phase accurately models money flow in business networks.

Conclusions:

  • Nonlinear transport in complex networks can exhibit distinct phases.
  • Network topology plays a crucial role in determining transport behavior.
  • The generalized gravity interaction model provides a framework for understanding real-world economic flows.