Synchronization in dynamical networks with unconstrained structure switching

Charo del Genio; Miguel Romance; Regino Criado; Stefano Boccaletti

doi:10.1103/PhysRevE.92.062819

Synchronization in dynamical networks with unconstrained structure switching

Charo del Genio, Miguel Romance, Regino Criado, Stefano Boccaletti

School of Computing, Electronics and Maths

Research output: Contribution to journal › Article

8 Citations (Scopus)

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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.

Original language	English
Article number	062819
Journal	Physical Review E
Volume	92
DOIs	https://doi.org/10.1103/PhysRevE.92.062819
Publication status	Published - 15 Dec 2015

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Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

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10.1103/PhysRevE.92.062819

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title = "Synchronization in dynamical networks with unconstrained structure switching",

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.",

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