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

Résultats de recherche: Contribution à un journal/une revueArticleRevue par des pairs

Résumé

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.

langue originaleAnglais
Pages (de - à)230-249
Nombre de pages20
journalPhysica A: Statistical Mechanics and its Applications
Volume462
Les DOIs
Etat de la publicationPublié - 17 juin 2016

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