Turing patterns in multiplex networks

Malbor Asllani, Daniel M. Busiello, Timoteo Carletti, Duccio Fanelli, Gwendoline Planchon

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Abstract

The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The interlayer diffusion constants act as a small parameter in the expansion and the unperturbed state coincides with the limiting setting where the multiplex layers are decoupled. The interaction between adjacent layers can seed the instability of a homogeneous fixed point, yielding self-organized patterns which are instead impeded in the limit of decoupled layers. Patterns on individual layers can also fade away due to cross-talking between layers. Analytical results are compared to direct simulations.

Original languageEnglish
Article number042814
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume90
Issue number4
DOIs
Publication statusPublished - 27 Oct 2014

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Keywords

  • turing patter
  • networks
  • multiplex networks
  • reaction-diffusion
  • non linear dynamics

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