Theory of Turing Patterns on Time Varying Networks

Julien Petit, Ben Lauwens, Duccio Fanelli, Timoteo Carletti

Research output: Contribution to journalLetter

23 Downloads (Pure)

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 languageEnglish
Article number148301
Pages (from-to)148301-1 148301-5
Number of pages5
JournalPhysical review letters
Volume119
Issue number14
DOIs
Publication statusPublished - 4 Oct 2017

Fingerprint

tuning
perturbation
predictions

Keywords

  • nonlinear dynamics
  • time varying networks
  • pattern formation
  • Turing patterns

Cite this

Petit, Julien ; Lauwens, Ben ; Fanelli, Duccio ; Carletti, Timoteo. / Theory of Turing Patterns on Time Varying Networks. In: Physical review letters. 2017 ; Vol. 119, No. 14. pp. 148301-1 148301-5.
@article{7741d7ec3ad3491297e1372a4e605a64,
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",
year = "2017",
month = "10",
day = "4",
doi = "https://doi.org/10.1103/PhysRevLett.119.148301",
language = "English",
volume = "119",
pages = "148301--1 148301--5",
journal = "Physical review letters",
issn = "0031-9007",
publisher = "American Physical Society",
number = "14",

}

Theory of Turing Patterns on Time Varying Networks. / Petit, Julien; Lauwens, Ben; Fanelli, Duccio; Carletti, Timoteo.

In: Physical review letters, Vol. 119, No. 14, 148301, 04.10.2017, p. 148301-1 148301-5.

Research output: Contribution to journalLetter

TY - JOUR

T1 - Theory of Turing Patterns on Time Varying Networks

AU - Petit, Julien

AU - Lauwens, Ben

AU - Fanelli, Duccio

AU - Carletti, Timoteo

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 - https://doi.org/10.1103/PhysRevLett.119.148301

DO - https://doi.org/10.1103/PhysRevLett.119.148301

M3 - Letter

VL - 119

SP - 148301-1 148301-5

JO - Physical review letters

JF - Physical review letters

SN - 0031-9007

IS - 14

M1 - 148301

ER -