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

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

Physica A: Statistical Mechanics and its Applications, 2016, vol. 462, issue C, 230-249

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.

Keywords: Turing patterns; Nonlinear dynamics; Spatio-temporal patterns; Complex networks; Delay differential equations (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:462:y:2016:i:c:p:230-249

DOI: 10.1016/j.physa.2016.06.003

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