Homogeneous-per-layer patterns in multiplex networks

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 patterns, made of alternating homogeneous layers of networks, 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-homogeneous 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.