Coarse-grained patterns in multiplex networks

TL;DR

This paper investigates new coarse-grained patterns in multiplex networks, revealing how layer stability and pattern formation depend on inter-layer diffusion and perturbations, with implications for multiplex system dynamics.

Contribution

It introduces a novel class of layer-homogeneous patterns and analyzes their stability and formation mechanisms in multiplex networks.

Findings

Identification of a tricritical point in stability diagrams.

Discovery of alternating homogeneous layer patterns.

Layer stability influenced by intra- and inter-layer diffusion.

Abstract

A new class of patterns for multiplex networks is studied, which consists in a collection of different homogeneous states each referred to a distinct layer. The associated stability diagram exhibits a tricritical point, as a function of the inter-layer diffusion coefficients. The coarse-grained patterns made of alternating homogenous layers, are dynamically selected via non homogeneous perturbations superposed to the underlying, globally homogeneous, fixed point and by properly modulating the coupling strength between layers. Furthermore, layer-homogenous fixed points can turn unstable following a mechanism \`a la Turing, instigated by the intra-layer diffusion. This novel class of solutions enriches the spectrum of dynamical phenomena as displayed within the variegated realm of multiplex science.