Theory of Turing Patterns on Time Varying Networks

Julien Petit; Ben Lauwens; Duccio Fanelli; Timoteo Carletti

doi:10.1103/PhysRevLett.119.148301

Theory of Turing Patterns on Time Varying Networks

Julien Petit, Ben Lauwens, Duccio Fanelli, Timoteo Carletti

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Résumé

The process of pattern formation for a multispecies model anchored on a time varying network is studied. A nonhomogeneous perturbation superposed to an homogeneous stable fixed point can be amplified following the Turing mechanism of instability, solely instigated by the network dynamics. By properly tuning the frequency of the imposed network evolution, one can make the examined system behave as its averaged counterpart, over a finite time window. This is the key observation to derive a closed analytical prediction for the onset of the instability in the time dependent framework. Continuously and piecewise constant periodic time varying networks are analyzed, setting the framework for the proposed approach. The extension to nonperiodic settings is also discussed.

langue originale	Anglais
Numéro d'article	148301
Pages (de - à)	148301-1 148301-5
Nombre de pages	5
journal	Physical review letters
Volume	119
Numéro de publication	14
Les DOIs	https://doi.org/10.1103/PhysRevLett.119.148301
Etat de la publication	Publié - 4 oct. 2017

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10.1103/PhysRevLett.119.148301

PetitEtAl_AllAccepted author manuscript, 5,24 MB

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.148301

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
Projet: Recherche

2 Participation à un atelier/workshop, un séminaire, un cours
2 Discours invité

A journey in the zoo of Turing patterns
Timoteo Carletti (Orateur invité)
23 janv. 2024
Activité: Discours ou présentation › Discours invité
SIAM Conference Dynamical Systems
Timoteo Carletti (Participant)
19 mai 2019 → 23 mai 2019
Activité: Participation ou organisation d'un événement › Participation à un atelier/workshop, un séminaire, un cours
SIAM Conference Dynamical Systems
Timoteo Carletti (Conférencier)
19 mai 2019
Activité: Participation ou organisation d'un événement › Participation à un atelier/workshop, un séminaire, un cours

Foundations of diffusion and instabilities in nonlinear evolution equations on temporal graphs and graphons
Auteur: PETIT, J., 25 juin 2020
Superviseur: Carletti, T. (Promoteur), Lauwens, B. (Personne externe) (Promoteur), MAUROY, A. (Président), Fanelli, D. (Personne externe) (Jury), Nakao, H. (Personne externe) (Jury) & Gallant, J. (Personne externe) (Jury)
Student thesis: Doc types › Docteur en Sciences

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Contient cette citation

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title = "Theory of Turing Patterns on Time Varying Networks",

abstract = "The process of pattern formation for a multispecies model anchored on a time varying network is studied. A nonhomogeneous perturbation superposed to an homogeneous stable fixed point can be amplified following the Turing mechanism of instability, solely instigated by the network dynamics. By properly tuning the frequency of the imposed network evolution, one can make the examined system behave as its averaged counterpart, over a finite time window. This is the key observation to derive a closed analytical prediction for the onset of the instability in the time dependent framework. Continuously and piecewise constant periodic time varying networks are analyzed, setting the framework for the proposed approach. The extension to nonperiodic settings is also discussed.",

keywords = "nonlinear dynamics, time varying networks, pattern formation, Turing patterns",

author = "Julien Petit and Ben Lauwens and Duccio Fanelli and Timoteo Carletti",

note = "Funding Information: The work of T. C. presents research results of the Belgian Network Dynamical Systems, Control, and Optimization (DYSCO), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The scientific responsibility rests with its author(s). D. F. acknowledges financial support from H2020-MSCA-ITN-2015 Project No. COSMOS 642563. Publisher Copyright: {\textcopyright} 2017 American Physical Society.",

year = "2017",

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doi = "10.1103/PhysRevLett.119.148301",

language = "English",

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T1 - Theory of Turing Patterns on Time Varying Networks

AU - Petit, Julien

AU - Lauwens, Ben

AU - Fanelli, Duccio

AU - Carletti, Timoteo

N1 - Funding Information: The work of T. C. presents research results of the Belgian Network Dynamical Systems, Control, and Optimization (DYSCO), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The scientific responsibility rests with its author(s). D. F. acknowledges financial support from H2020-MSCA-ITN-2015 Project No. COSMOS 642563. Publisher Copyright: © 2017 American Physical Society.

PY - 2017/10/4

Y1 - 2017/10/4

N2 - The process of pattern formation for a multispecies model anchored on a time varying network is studied. A nonhomogeneous perturbation superposed to an homogeneous stable fixed point can be amplified following the Turing mechanism of instability, solely instigated by the network dynamics. By properly tuning the frequency of the imposed network evolution, one can make the examined system behave as its averaged counterpart, over a finite time window. This is the key observation to derive a closed analytical prediction for the onset of the instability in the time dependent framework. Continuously and piecewise constant periodic time varying networks are analyzed, setting the framework for the proposed approach. The extension to nonperiodic settings is also discussed.

AB - The process of pattern formation for a multispecies model anchored on a time varying network is studied. A nonhomogeneous perturbation superposed to an homogeneous stable fixed point can be amplified following the Turing mechanism of instability, solely instigated by the network dynamics. By properly tuning the frequency of the imposed network evolution, one can make the examined system behave as its averaged counterpart, over a finite time window. This is the key observation to derive a closed analytical prediction for the onset of the instability in the time dependent framework. Continuously and piecewise constant periodic time varying networks are analyzed, setting the framework for the proposed approach. The extension to nonperiodic settings is also discussed.

KW - nonlinear dynamics

KW - time varying networks

KW - pattern formation

KW - Turing patterns

U2 - 10.1103/PhysRevLett.119.148301

DO - 10.1103/PhysRevLett.119.148301

M3 - Letter

SN - 0031-9007

VL - 119

SP - 148301-1 148301-5

JO - Physical review letters

JF - Physical review letters

IS - 14

M1 - 148301

ER -

Theory of Turing Patterns on Time Varying Networks

Résumé

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Empreinte digitale

Projets

PAI n°P7/19 - DYSCO: Dynamical systems, control and optimization (DYSCO)

Activités

A journey in the zoo of Turing patterns

SIAM Conference Dynamical Systems

SIAM Conference Dynamical Systems

Thèses de l'étudiant

Foundations of diffusion and instabilities in nonlinear evolution equations on temporal graphs and graphons

Contient cette citation