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Turing patterns in multiplex networks.

Malbor Asllani1, Daniel M Busiello2, Timoteo Carletti3

  • 1Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy and Dipartimento di Fisica e Astronomia, University of Florence, INFN and CSDC, Via Sansone 1, 50019 Sesto Fiorentino, Florence, Italy.

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Summary
This summary is machine-generated.

This study develops a theory for pattern formation in reaction-diffusion systems on multiplex networks. Interlayer diffusion can induce self-organized patterns, contrasting with decoupled layers where patterns are hindered.

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Area of Science:

  • Mathematical modeling
  • Complex systems
  • Network theory

Background:

  • Reaction-diffusion systems are fundamental to understanding pattern formation in nature.
  • Multiplex networks, with multiple interacting layers, present unique challenges for modeling.
  • Previous studies often simplified networks, neglecting crucial interlayer dynamics.

Purpose of the Study:

  • To develop a theoretical framework for pattern formation in reaction-diffusion systems on multiplex networks.
  • To investigate the role of interlayer diffusion in pattern emergence and stability.
  • To analyze how network topology influences self-organized pattern formation.

Main Methods:

  • A perturbative approach was employed to analyze the reaction-diffusion system.
  • Interlayer diffusion constants were treated as small parameters for expansion.
  • Analytical results were validated through direct numerical simulations.

Main Results:

  • Interlayer diffusion can destabilize homogeneous states, leading to self-organized pattern formation.
  • Decoupled layers (zero interlayer diffusion) impede pattern formation.
  • Cross-talk between layers can cause patterns on individual layers to disappear.

Conclusions:

  • Interlayer coupling is a critical factor in pattern dynamics on multiplex networks.
  • The developed theory provides a foundation for understanding complex pattern formation in multi-layered systems.
  • This work highlights the importance of considering network structure in reaction-diffusion processes.