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The relationship between clustering and networked Turing patterns.

Xiaofeng Luo1, Guiquan Sun1,2,3, Runzi He1

  • 1School of Mathematics, North University of China, Shanxi, Taiyuan 030051, China.

Chaos (Woodbury, N.Y.)
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Summary
This summary is machine-generated.

Network clustering affects Turing patterns in prey-predator models. Increased clustering causes a linear decay in patterns, impacting ecosystem stability and refuges.

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Area of Science:

  • Network science
  • Mathematical biology
  • Ecology

Background:

  • Networked Turing patterns are influenced by topology, like average degree.
  • The specific impact of clustering on these patterns is not well understood.
  • Prey-predator models are used to study pattern formation in ecological networks.

Purpose of the Study:

  • To investigate the relationship between network clustering and Turing pattern formation.
  • To understand how clustering coefficients affect the stability of prey-predator systems.
  • To provide insights into controlling pattern formation in real-world systems.

Main Methods:

  • Utilized classical prey-predator models.
  • Analyzed the influence of global clustering coefficients on Turing patterns.
  • Examined pattern behavior under varying node density distributions.

Main Results:

  • A linear decay in Turing patterns was observed with increasing global clustering coefficients when node densities were balanced.
  • This linear decay may not hold if high-density nodes are treated as low-density nodes.
  • Clustering significantly impacts the qualitative assessment of Turing pattern formation.

Conclusions:

  • Clustering coefficients play a crucial role in the formation and stability of networked Turing patterns.
  • Understanding clustering's impact can explain the stabilizing effect of refuges in ecosystems.
  • Results offer a network-based perspective for predicting and controlling ecological pattern formation.