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

Research output: Contribution to journal › Letter › peer-review

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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.

Original language	English
Article number	148301
Pages (from-to)	148301-1 148301-5
Number of pages	5
Journal	Physical review letters
Volume	119
Issue number	14
DOIs	https://doi.org/10.1103/PhysRevLett.119.148301
Publication status	Published - 4 Oct 2017

Keywords

nonlinear dynamics
time varying networks
pattern formation
Turing patterns

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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
Project: Research

2 Participation in workshop, seminar, course
1 Invited talk

SIAM Conference Dynamical Systems
Timoteo Carletti (Participant)
19 May 2019 → 23 May 2019
Activity: Participating in or organising an event types › Participation in workshop, seminar, course
SIAM Conference Dynamical Systems
Timoteo Carletti (Speaker)
19 May 2019
Activity: Participating in or organising an event types › Participation in workshop, seminar, course
Turing patterns on time varying networks
Timoteo Carletti (Speaker)
18 Jul 2018
Activity: Talk or presentation types › Invited talk

Foundations of diffusion and instabilities in nonlinear evolution equations on temporal graphs and graphons
Author: PETIT, J., 25 Jun 2020
Supervisor: 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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Cite this

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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",

month = oct,

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doi = "10.1103/PhysRevLett.119.148301",

language = "English",

volume = "119",

pages = "148301--1 148301--5",

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TY - JOUR

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

Abstract

Keywords

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Projects

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

Activities

SIAM Conference Dynamical Systems

SIAM Conference Dynamical Systems

Turing patterns on time varying networks

Student theses

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

Cite this