The multiplex decomposition: An analytic framework for multilayer dynamical networks
| Autor: | Volker Mehrmann, Serhiy Yanchuk, Rico Berner, Eckehard Schöll |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Computer science
Diagonal MathematicsofComputing_NUMERICALANALYSIS FOS: Physical sciences Complex network Topology Nonlinear Sciences - Adaptation and Self-Organizing Systems Modeling and Simulation Decomposition (computer science) ddc:530 Multiplex Adjacency matrix Adaptation and Self-Organizing Systems (nlin.AO) Analysis Master stability function 34D06 37Nxx 92B20 Computer Science::Information Theory |
| Popis: | First Published in SIAM Journal on Applied Dynamical Systems in Volume 20, Issue 4 (2021), published by the Society for Industrial and Applied Mathematics (SIAM).Copyright © by SIAM. Unauthorized reproduction of this article is prohibited. 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. |
| Databáze: | OpenAIRE |
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