Theory of Turing Patterns on Time Varying Networks

Julien Petit, Ben Lauwens, Duccio Fanelli, Timoteo Carletti

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Abstract

The process of pattern formation for a multispecies model anchored on a time varying network is studied. A nonhomogeneous perturbation superposed to an homogeneous stable fixed point can be amplified following the Turing mechanism of instability, solely instigated by the network dynamics. By properly tuning the frequency of the imposed network evolution, one can make the examined system behave as its averaged counterpart, over a finite time window. This is the key observation to derive a closed analytical prediction for the onset of the instability in the time dependent framework. Continuously and piecewise constant periodic time varying networks are analyzed, setting the framework for the proposed approach. The extension to nonperiodic settings is also discussed.
Original languageEnglish
Article number148301
Pages (from-to)148301-1 148301-5
Number of pages5
JournalPhysical review letters
Volume119
Issue number14
DOIs
Publication statusPublished - 4 Oct 2017

Keywords

  • nonlinear dynamics
  • time varying networks
  • pattern formation
  • Turing patterns

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