English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We present a general framework to study stability of the synchronous solutionfor a hypernetwork of coupled dynamical systems. We are able to reduce thedimensionality of the problem by using simultaneous block-diagonalization ofmatrices. We obtain necessary and sufficient conditions for stability of thesynchronous solution in terms of a set of lower-dimensional problems and testthe predictions of our low-dimensional analysis through numerical simulations.Under certain conditions, this technique may yield a substantial reduction ofthe dimensionality of the problem. For example, for a class of dynamicalhypernetworks analyzed in the paper, we discover that arbitrarily largenetworks can be reduced to a collection of subsystems of dimensionality no morethan 2. We apply our reduction techique to a number of different examples,including a class of undirected unweighted hypermotifs of three nodes.

Synchronization of dynamical hypernetworks: dimensionality reduction through simultaneous block-diagonalization of matrices