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

A one-species time-delay reaction-diffusion system defined on a complex network is studied. Traveling waves are predicted to occur following a symmetry-breaking instability of a homogeneous stationary stable solution, subject to an external nonhomogeneous perturbation. These are generalized Turing-l...

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Bibliographic Details
Published in:	Europhysics letters 2015-09, Vol.111 (5), p.58002-p1-58002-p6
Main Authors:	Petit, Julien, Carletti, Timoteo, Asllani, Malbor, Fanelli, Duccio
Format:	Article
Language:	eng
Subjects:	89.75.Fb 89.75.Hc 89.75.Kd Byproducts Delay Differential equations Dynamical systems Instability Mathematical models Networks Stability
Online Access:	Get full text
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Summary:	A one-species time-delay reaction-diffusion system defined on a complex network is studied. Traveling waves are predicted to occur following a symmetry-breaking instability of a homogeneous stationary stable solution, subject to an external nonhomogeneous 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 equations. 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 network and with the inclusion of the delay.
ISSN:	0295-5075 1286-4854