Delay induced Turing-like waves for one species reaction-diffusion model on a network
Abstract
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.
Cite
@article{arxiv.1507.00976,
title = {Delay induced Turing-like waves for one species reaction-diffusion model on a network},
author = {Julien Petit and Timoteo Carletti and Mabor Asslani and Duccio Fanelli},
journal= {arXiv preprint arXiv:1507.00976},
year = {2015}
}