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Abstract
A one species time–delay reactiondiffusion 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 Turinglike 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 Wfunction. 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 WattsStrogatz networks and with the inclusion of the delay.
Original language  English 

Publisher  Namur center for complex systems 
Number of pages  9 
Volume  7 
Edition  15 
Publication status  Published  6 Jul 2015 
Publication series
Name  naXys Technical Report Series 

Publisher  University of Namur 
No.  15 
Volume  7 
Keywords
 nonlinear absorption
 spatiotemporal patterns
 Complex Networks
 delay differential equations
 Turing waves
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PAI n°P7/19  DYSCO: Dynamical systems, control and optimization (DYSCO)
WINKIN, J., Blondel, V., Vandewalle, J., Pintelon, R., Sepulchre, R., Vande Wouwer, A. & Sartenaer, A.
1/04/12 → 30/09/17
Project: Research
Equipment

High Performance Computing Technology Platform
Benoît Champagne (Manager)
Technological Platform High Performance ComputingFacility/equipment: Technological Platform