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Nonlinear consensus on networks : equilibria, effective resistance, and trees of motifs
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Homs-Dones, Marc, Devriendt, Karel and Lambiotte, Renaud (2021) Nonlinear consensus on networks : equilibria, effective resistance, and trees of motifs. SIAM Journal on Applied Dynamical Systems, 20 (3). pp. 1544-1570. doi:10.1137/20M1376844 ISSN 1536-0040.
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Official URL: http://dx.doi.org/10.1137/20M1376844
Abstract
We study a generic family of nonlinear dynamics on undirected networks generalizing linear consensus. We find a compact expression for its equilibrium points in terms of the topology of the network and classify their stability using the effective resistance of the underlying graph equipped with appropriate weights. Our general results are applied to some specific networks, namely trees, cycles, and complete graphs. When a network is formed by the union of two subnetworks joined in a single node, we show that the equilibrium points and stability in the whole network can be found by simply studying the smaller subnetworks instead. Applied recursively, this property opens the possibility of investigating dynamical behavior on families of networks made of trees of motifs.
Item Type: | Journal Article | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Journal or Publication Title: | SIAM Journal on Applied Dynamical Systems | ||||||
Publisher: | Society for Industrial and Applied Mathematics | ||||||
ISSN: | 1536-0040 | ||||||
Official Date: | 9 September 2021 | ||||||
Dates: |
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Volume: | 20 | ||||||
Number: | 3 | ||||||
Page Range: | pp. 1544-1570 | ||||||
DOI: | 10.1137/20M1376844 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Copyright Holders: | © 2021, Society for Industrial and Applied Mathematics Read More: https://epubs.siam.org/doi/abs/10.1137/20M1376844 |
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