Aspects of Transitions in the Dynamics and Topology of Multilayer Networks

I will review three different investigations into Multilayer Networks performed as part of the LASAGNE initiative. The multilayer structure couples together several networks to create a framework more natural for analysing processes occuring at different timescales or with different dynamics. First, we will consider how the multilayer structure influences the transitions found in the Coevolving Voter Model (CVM, F. Vazquez et al, PRL 100, 108702 (2008)). The CVM is a prototype for a system where dynamics on the network are interdependent with the dynamics of the network. We find that coupling together two such identical systems preserves but offsets the transitions, but that joining networks with differing topological timescales lead to novel fragmentation pattern found on the more topologically-dynamic layer.

We will then show how to obtain the same 'shattered' fragmentation pattern without the use of multilayer structure, but instead through the targeting the noise to a subset of nodes.
Finally, we will explain the standard methodology for considering timescales of diffusive processes on multilayer networks, and show our ongoing results on the influence of the intralayer and interlayer ensembles, as well as the layer connectivity strategy, on the transition found in the second smallest eigenvalue of the multilayer Laplacian. Briefly, we find that the timescales can be controlled not only by introducing interlayer correlations, but also by the order in which the layers are connected.