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The multiplex decomposition: an analytic framework for multilayer dynamical networks. (English) Zbl 1485.34105

A multiplex network is a network composed of multiple layers such that the number of nodes in all layers is the same and connections between layers are only between a node in one layer and the same node in a different layer. For networks where the adjacency matrices describing connectivity within layers are simultaneously triagonalizable, the authors relate the spectrum of the multiplex network to the spectrum of the individual adjacency matrices. The application of this is to the stability of a synchronous solution of the multiplex network, giving a generalisation of the master stability function to such networks. An an application a duplex network of FitzHugh-Nagumo oscillators is studied.

MSC:

34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34D06 Synchronization of solutions to ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
05C82 Small world graphs, complex networks (graph-theoretic aspects)
92C20 Neural biology
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