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arXiv · 1507.00976

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

Julien Petit·Timoteo Carletti·Mabor Asslani·Duccio Fanelli
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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.

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Julien Petit, Timoteo Carletti, Mabor Asslani, Duccio Fanelli. 2015-07-03. Delay induced Turing-like waves for one species reaction-diffusion model on a network. https://doi.org/10.1209/0295-5075/111/58002

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