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Abstract

Multiplex networks are networks composed of multiple layers such that the number of nodes in all
layers is the same and the adjacency matrices between the layers are diagonal. We consider the
special class of multiplex networks where the adjacency matrices for each layer are simultaneously
triagonalizable. For such networks, we derive the relation between the spectrum of the multiplex
network and the eigenvalues of the individual layers. As an application, we propose a generalized
master stability approach that allows for a simplified, low-dimensional description of the stability
of synchronized solutions in multiplex networks. We illustrate our result with a duplex network
of FitzHugh--Nagumo oscillators. In particular, we show how interlayer interaction can lead to
stabilization or destabilization of the synchronous state. Finally, we give explicit conditions for the
stability of synchronous solutions in duplex networks of linear diffusive systems.