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

Résultats de recherche: Livre/Rapport/RevueAutre rapport

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Résumé

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.
langue originaleAnglais
EditeurNamur center for complex systems
Nombre de pages9
Volume7
Edition15
étatPublié - 6 juil. 2015

Série de publications

NomnaXys Technical Report Series
EditeurUniversity of Namur
Numéro15
Volume7

Empreinte digitale

direct numerical simulation
traveling waves
dynamic models
broken symmetry
differential equations
inclusions
perturbation
predictions

Citer ceci

Petit, J., Carletti, T., Asllani, M., & Fanelli, D. (2015). Delay induced Turing-like waves for one species reaction–diffusion model on a network. (15 Ed.) (naXys Technical Report Series; Vol 7, Numéro 15). Namur center for complex systems.
Petit, Julien ; Carletti, Timoteo ; Asllani, Malbor ; Fanelli, Duccio. / Delay induced Turing-like waves for one species reaction–diffusion model on a network. 15 Ed. Namur center for complex systems, 2015. 9 p. (naXys Technical Report Series; 15).
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title = "Delay induced Turing-like waves for one species reaction–diffusion model on a network",
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.",
keywords = "nonlinear absorption, spatio-temporal patterns, Complex Networks, delay differential equations, Turing waves",
author = "Julien Petit and Timoteo Carletti and Malbor Asllani and Duccio Fanelli",
year = "2015",
month = "7",
day = "6",
language = "English",
volume = "7",
series = "naXys Technical Report Series",
publisher = "Namur center for complex systems",
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Petit, J, Carletti, T, Asllani, M & Fanelli, D 2015, Delay induced Turing-like waves for one species reaction–diffusion model on a network. naXys Technical Report Series, Numéro 15, VOL. 7, VOL. 7, 15 edn, Namur center for complex systems.

Delay induced Turing-like waves for one species reaction–diffusion model on a network. / Petit, Julien; Carletti, Timoteo; Asllani, Malbor; Fanelli, Duccio.

15 Ed. Namur center for complex systems, 2015. 9 p. (naXys Technical Report Series; Vol 7, Numéro 15).

Résultats de recherche: Livre/Rapport/RevueAutre rapport

TY - BOOK

T1 - Delay induced Turing-like waves for one species reaction–diffusion model on a network

AU - Petit, Julien

AU - Carletti, Timoteo

AU - Asllani, Malbor

AU - Fanelli, Duccio

PY - 2015/7/6

Y1 - 2015/7/6

N2 - 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.

AB - 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.

KW - nonlinear absorption

KW - spatio-temporal patterns

KW - Complex Networks

KW - delay differential equations

KW - Turing waves

M3 - Other report

VL - 7

T3 - naXys Technical Report Series

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

PB - Namur center for complex systems

ER -

Petit J, Carletti T, Asllani M, Fanelli D. Delay induced Turing-like waves for one species reaction–diffusion model on a network. 15 Ed. Namur center for complex systems, 2015. 9 p. (naXys Technical Report Series; 15).