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Self-organized transport in noisy dynamic networks.

Frederic Folz1, Kurt Mehlhorn2, Giovanna Morigi1

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Noise can help nonlinear networks self-organize into robust structures. Different nonlinear functions and noise levels create unique network behaviors and solutions, highlighting the activation function

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Area of Science:

  • Complex Networks
  • Nonlinear Dynamics
  • Network Science

Background:

  • Multicommodity transport networks are susceptible to noise and nonlinear dynamics.
  • Edge capacities in such networks can fluctuate based on local current.
  • Understanding network self-organization is crucial for robust system design.

Purpose of the Study:

  • To numerically investigate multicommodity transport in noisy, nonlinear networks.
  • To explore how different nonlinear functions influence network self-organization.
  • To identify the role of noise in promoting robust network topologies.

Main Methods:

  • Numerical simulation of multicommodity flow in nonlinear networks.
  • Analysis of network self-organization under varying noise levels.
  • Examination of three distinct nonlinear activation functions.

Main Results:

  • Noise facilitates self-organization into more robust topologies than noiseless dynamics.
  • Specific nonlinear functions lead to continuous or discontinuous responses to demand.
  • Network behavior exhibits single or multistable solutions depending on nonlinearity and noise.

Conclusions:

  • Noise plays a critical role in network self-organization and topology robustness.
  • The choice of activation function significantly impacts noise-assisted phenomena.
  • Nonlinear dynamics combined with noise offer pathways to enhanced network resilience.