Projects per year
Abstract
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.
Original language | English |
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Article number | 58002 |
Number of pages | 9 |
Journal | Europhysics Letters |
Volume | 111 |
Issue number | 5 |
Publication status | Published - 18 Sept 2015 |
Keywords
- nonlinear absorption
- spatio-temporal 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
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High Performance Computing Technology Platform
Benoît Champagne (Manager)
Technological Platform High Performance ComputingFacility/equipment: Technological Platform
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Control of self-organized patterns in complex networks
Timoteo Carletti (Speaker)
18 Jul 2017Activity: Participating in or organising an event types › Participation in workshop, seminar, course
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Control of self-organized patterns in complex networks
Timoteo Carletti (Organiser)
18 Jul 2017Activity: Participating in or organising an event types › Participation in workshop, seminar, course
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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
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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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