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Synchronization in dynamical networks with unconstrained structure switching

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Del Genio, Charo I., Romance, Miguel, Criado, Regino and Boccaletti, Stefano (2015) Synchronization in dynamical networks with unconstrained structure switching. Physical Review E, 92 (6). doi:10.1103/PhysRevE.92.062819

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Official URL: http://dx.doi.org/10.1103/PhysRevE.92.062819

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Abstract

We provide a rigorous solution to the problem of constructing a structural evolution for a network of coupled identical dynamical units that switches between specified topologies without constraints on their structure. The evolution of the structure is determined indirectly from a carefully built transformation of the eigenvector matrices of the coupling Laplacians, which are guaranteed to change smoothly in time. In turn, this allows one to extend the master stability function formalism, which can be used to assess the stability of a synchronized state. This approach is independent from the particular topologies that the network visits, and is not restricted to commuting structures. Also, it does not depend on the time scale of the evolution, which can be faster than, comparable to, or even secular with respect to the dynamics of the units.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Q Science > QH Natural history
Q Science > QP Physiology
Divisions: Faculty of Science > Life Sciences (2010- )
Library of Congress Subject Headings (LCSH): Topological dynamics , Neural networks (Neurobiology), Biotic communities
Journal or Publication Title: Physical Review E
Publisher: American Physical Society
ISSN: 1539-3755
Official Date: 15 December 2015
Dates:
DateEvent
15 December 2015Published
30 November 2015Accepted
8 August 2014Submitted
Volume: 92
Number: 6
DOI: 10.1103/PhysRevE.92.062819
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Funder: Seventh Framework Programme (European Commission) (FP7)
Grant number: 288021 (FP7)

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