Delay induced Turing-like waves for one species reaction–diffusion model on a network

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A one species time–delay reaction-diffusion system defined on a complex networks is studied. Travelling waves are predicted to occur as follows a symmetry breaking instability of an homogenous stationary stable solution, subject to an external non homogenous perturbation. These are generalized Turing-like waves that materialize in a single species populations dynamics model, as the unexpected byproduct of the imposed delay in the diffusion part. Sufficient conditions for the onset of the instability are mathematically provided by performing a linear stability analysis adapted to time delayed differential equation. The method here developed exploits the properties of the Lambert W-function. The prediction of the theory are confirmed by direct numerical simulation carried out for a modified version of the classical Fisher model, defined on a Watts-Strogatz networks and with the inclusion of the delay.
langue originaleAnglais
EditeurNamur center for complex systems
Nombre de pages9
Etat de la publicationPublié - 6 juil. 2015

Série de publications

NomnaXys Technical Report Series
EditeurUniversity of Namur

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