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arXiv · 1603.07122

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
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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 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.

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Julien Petit, Malbor Asllani, Duccio Fanelli, Ben Lauwens, Timoteo Carletti. 2016-03-23. Pattern formation in a two-component reaction-diffusion system with delayed processes on a network. https://doi.org/10.1016/j.physa.2016.06.003

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