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Abstract
A onespecies timedelay reactiondiffusion system defined on a complex network is studied. Traveling waves are predicted to occur following a symmetrybreaking instability of a homogeneous stationary stable solution, subject to an external nonhomogeneous perturbation. These are generalized Turinglike waves that materialize in a singlespecies 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 timedelayed differential equations. 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 network and with the inclusion of the delay.
Original language  English 

Article number  58002 
Number of pages  9 
Journal  Europhysics Letters 
Volume  111 
Issue number  5 
Publication status  Published  18 Sep 2015 
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

Control of selforganized patterns in complex networks
Timoteo Carletti (Speaker)
18 Jul 2017Activity: Participating in or organising an event types › Participation in workshop, seminar, course

Control of selforganized patterns in complex networks
Timoteo Carletti (Organiser)
18 Jul 2017Activity: Participating in or organising an event types › Participation in workshop, seminar, course

IAP VIII / 19 DYSCO  Dynamical SYStems Control and Optimization DYSCO Study day
Timoteo Carletti (Speaker)
1 Dec 2016Activity: Participating in or organising an event types › Participation to a Symposium, a study Day
Student Theses

Foundations of diffusion and instabilities in nonlinear evolution equations on temporal graphs and graphons
Author: PETIT, J., 25 Jun 2020Supervisor: Carletti, T. (Supervisor), Lauwens, B. (External person) (Supervisor), MAUROY, A. (President), Fanelli, D. (External person) (Jury), Nakao, H. (External person) (Jury) & Gallant, J. (External person) (Jury)
Student thesis: Doc types › Doctor of Sciences
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