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Predictable topological sensitivity of Turing patterns on graphs.

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Summary
This summary is machine-generated.

Network topology significantly impacts Turing patterns, which are self-organized collective patterns in reaction-diffusion systems. Even minor network changes can drastically alter pattern diversity, with eigenvalue degeneracy being a key predictor.

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Area of Science:

  • Complex Systems
  • Network Science
  • Mathematical Biology

Background:

  • Reaction-diffusion systems generate self-organized patterns called Turing patterns.
  • Dynamical processes on networks are increasingly used to study these patterns.

Purpose of the Study:

  • Investigate how network topology influences Turing pattern diversity.
  • Identify key factors determining sensitivity to topological changes.

Main Methods:

  • Systematic numerical experiments on networks.
  • Analysis of graph Laplacian spectrum and linearized dynamics.
  • Exploration of attractor landscape sensitivity.

Main Results:

  • Minor network alterations (single link removal/rewiring) cause significant changes in pattern diversity.
  • Topological sensitivity can be predicted from spectral properties and linearized dynamics.
  • Eigenvalue degeneracy or growth rate, not the number of unstable modes, is the primary determinant.

Conclusions:

  • Network structure critically shapes the diversity of emergent Turing patterns.
  • Predictive methods for pattern diversity exist, bypassing full dynamical simulations.
  • Understanding spectral properties is key to controlling pattern formation in networked systems.