Turing patterns in multiplex networks

TL;DR

This paper develops a perturbative theory for pattern formation in reaction-diffusion systems on multiplex networks, revealing how inter-layer interactions can induce or suppress Turing patterns.

Contribution

It introduces a novel analytical approach to understand Turing pattern emergence in multiplex networks using perturbation theory based on intra-layer diffusion constants.

Findings

Inter-layer interactions can trigger Turing instabilities.

Decoupled layers do not exhibit patterns, but coupling can induce them.

Cross-talk between layers can suppress existing patterns.

Abstract

The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The intra-layer diffusion constants act as 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 an 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.