Author
Homs-Dones, M
Devriendt, K
Lambiotte, R
Journal title
SIAM Journal on Applied Dynamical Systems
DOI
10.1137/20M1376844
Issue
3
Volume
20
Last updated
2022-08-05T08:46:48.687+01:00
Page
1544-1570
Abstract
We study a generic family of non-linear dynamics on networks generalising
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 sub-networks
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 sub-networks
instead. Applied recursively, this property opens the possibility to
investigate the dynamical behaviour on families of networks made of trees of
motifs, including hypertrees.
Symplectic ID
1129434
Favourite
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Publication type
Journal Article
Publication date
09 Sep 2021
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