Ising dynamics on multilayer networks with heterogeneous layers.

Multilayer networks provide a framework to study complex systems with multiple types of interactions, multiple dynamical processes, and/or multiple subsystems. When studying a dynamical process on a multilayer network, it is important to consider how both layer structure and heterogeneity across layers impacts the overall dynamics. As a concrete example, we study Ising dynamics on multilayer networks and investigate how network structure affects its qualitative features. We focus primarily on multiplex networks, which are multilayer networks in which interlayer edges occur only between manifestations of the same entity on different layers, although we also consider one empirical example with a more general multilayer structure. We use numerical simulations and a mean-field approximation to examine the steady-state behavior of the Ising dynamics as a function of temperature (which is a key model parameter) for a variety of two-layer multilayer networks from both models and empirical data. We examine both the steady-state behavior and a metastable state in which the two layers are anti-aligned, and we explore the effects of interlayer coupling strength and structural heterogeneity. In synthetic multilayer networks with core--periphery structure, we show that interlayer edges that involve peripheral nodes can exert more influence than interlayer edges that involve only core nodes. Finally, we consider empirical multilayer networks from biological and social systems. Our work illustrates how heterogeneity across the layers of a multilayer network influences dynamics on the whole network.