Privacy Policy Disclaimer
  Advanced SearchBrowse




Journal Article

The Multiplex Decomposition: An Analytic Framework for Multilayer Dynamical Networks


Berner,  Rico
External Organizations;

Mehrmann,  Volker
External Organizations;


Schöll,  Eckehard
Potsdam Institute for Climate Impact Research;

Yanchuk,  Serhiy
External Organizations;

External Ressource
No external resources are shared
Fulltext (public)
There are no public fulltexts stored in PIKpublic
Supplementary Material (public)
There is no public supplementary material available

Berner, R., Mehrmann, V., Schöll, E., Yanchuk, S. (2021): The Multiplex Decomposition: An Analytic Framework for Multilayer Dynamical Networks. - SIAM Journal on Applied Dynamical Systems, 20, 4, 1752-1772.

Cite as: https://publications.pik-potsdam.de/pubman/item/item_26489
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.