Turing patterns in multiplex networks

Malbor Asllani; Daniel M. Busiello; Timoteo Carletti; Duccio Fanelli; Gwendoline Planchon

doi:10.1103/PhysRevE.90.042814

Turing patterns in multiplex networks

Malbor Asllani, Daniel M. Busiello, Timoteo Carletti, Duccio Fanelli, Gwendoline Planchon

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

Abstract

The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The interlayer diffusion constants act as a small parameter in the expansion and the unperturbed state coincides with the limiting setting where the multiplex layers are decoupled. The interaction between adjacent layers can seed the instability of a homogeneous fixed point, yielding self-organized patterns which are instead impeded in the limit of decoupled layers. Patterns on individual layers can also fade away due to cross-talking between layers. Analytical results are compared to direct simulations.

Original language	English
Article number	042814
Journal	Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics
Volume	90
Issue number	4
DOIs	https://doi.org/10.1103/PhysRevE.90.042814
Publication status	Published - 27 Oct 2014

Keywords

turing patter
networks
multiplex networks
reaction-diffusion
non linear dynamics

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10.1103/PhysRevE.90.042814

Cite this

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abstract = "The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The interlayer diffusion constants act as a small parameter in the expansion and the unperturbed state coincides with the limiting setting where the multiplex layers are decoupled. The interaction between adjacent layers can seed the instability of a homogeneous fixed point, yielding self-organized patterns which are instead impeded in the limit of decoupled layers. Patterns on individual layers can also fade away due to cross-talking between layers. Analytical results are compared to direct simulations.",

keywords = "turing patter, networks, multiplex networks, reaction-diffusion, non linear dynamics",

author = "Malbor Asllani and Busiello, {Daniel M.} and Timoteo Carletti and Duccio Fanelli and Gwendoline Planchon",

year = "2014",

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N2 - The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The interlayer diffusion constants act as a small parameter in the expansion and the unperturbed state coincides with the limiting setting where the multiplex layers are decoupled. The interaction between adjacent layers can seed the instability of a homogeneous fixed point, yielding self-organized patterns which are instead impeded in the limit of decoupled layers. Patterns on individual layers can also fade away due to cross-talking between layers. Analytical results are compared to direct simulations.

AB - The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The interlayer diffusion constants act as a small parameter in the expansion and the unperturbed state coincides with the limiting setting where the multiplex layers are decoupled. The interaction between adjacent layers can seed the instability of a homogeneous fixed point, yielding self-organized patterns which are instead impeded in the limit of decoupled layers. Patterns on individual layers can also fade away due to cross-talking between layers. Analytical results are compared to direct simulations.

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KW - non linear dynamics

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Turing patterns in multiplex networks

Abstract

Keywords

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Other files and links

Fingerprint

Dynamical systems analysis, modeling and simulation

Reaction-diffusion equations: the role of geometry and granularity

Workshop on Dynamical Processes on Complex Networks

Control of self-organized patterns in complex networks

Control of self-organized patterns in complex networks

Cite this

Turing patterns in multiplex networks

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Dynamical systems analysis, modeling and simulation

Reaction-diffusion equations: the role of geometry and granularity

Activities

Workshop on Dynamical Processes on Complex Networks

Control of self-organized patterns in complex networks

Control of self-organized patterns in complex networks

Cite this