Pattern formation in a two-component reaction–diffusion system with delayed processes on a network

Julien Petit, Malbor Asllani, Duccio Fanelli, Ben Lauwens, Timoteo Carletti

Research output: Contribution to journalArticle

Abstract

Reaction–diffusion systems with time-delay defined on complex networks have been studied in the framework of the emergence of Turing instabilities. The use of the Lambert W-function allowed us to get explicit analytic conditions for the onset of patterns as a function of the main involved parameters, the time-delay, the network topology and the diffusion coefficients. Depending on these parameters, the analysis predicts

whether the system will evolve towards a stationary Turing pattern or rather to a wave pattern associated to a Hopf bifurcation. The possible outcomes of the linear analysis overcome the respective limitations of the single-species case with delay, and that of the classical activator–inhibitor variant without delay. Numerical results gained from the Mimura–Murray model support the theoretical approach.

Original languageEnglish
Pages (from-to)230-249
Number of pages20
JournalPhysica A: Statistical Mechanics and its Applications
Volume462
DOIs
Publication statusPublished - 17 Jun 2016

Keywords

  • nonlinear dynamics
  • spatio-temporal patterns
  • Complex Networks
  • delay differential equations
  • Turing waves

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  • Projects

    PAI n°P7/19 - DYSCO: Dynamical systems, control and optimization (DYSCO)

    WINKIN, J., Blondel, V., Vandewalle, J., Pintelon, R., Sepulchre, R., Vande Wouwer, A. & SARTENAER, A.

    1/04/1230/09/17

    Project: Research

    Equipment

  • Activities

    • 4 Participation in workshop, seminar, course
    • 1 Participation to a Symposium, a study Day

    Control of self-organized patterns in complex networks

    Timoteo Carletti (Organiser)

    18 Jul 2017

    Activity: Participating in or organising an event typesParticipation in workshop, seminar, course

    Control of self-organized patterns in complex networks

    Timoteo Carletti (Speaker)

    18 Jul 2017

    Activity: Participating in or organising an event typesParticipation in workshop, seminar, course

    IAP VIII / 19 DYSCO - Dynamical SYStems Control and Optimization DYSCO Study day

    Timoteo Carletti (Speaker)

    1 Dec 2016

    Activity: Participating in or organising an event typesParticipation to a Symposium, a study Day

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