Robust partial synchronization of delay-coupled networks

Libo Su, Yanling Wei, Wim Michiels, Erik Steur, Henk Nijmeijer

Research output: Contribution to journalArticleAcademicpeer-review

6 Citations (Scopus)
128 Downloads (Pure)

Abstract

Networks of coupled systems may exhibit a form of incomplete synchronization called partial synchronization or cluster synchronization, which refers to the situation where only some, but not all, systems exhibit synchronous behavior. Moreover, due to perturbations or uncertainties in the network, exact partial synchronization in the sense that the states of the systems within each cluster become identical, cannot be achieved. Instead, an approximate synchronization may be observed, where the states of the systems within each cluster converge up to some bound, and this bound tends to zero if (the size of) the perturbations tends to zero. In order to derive sufficient conditions for this robustified notion of synchronization, which we refer to as practical partial synchronization, first, we separate the synchronization error dynamics from the network dynamics and interpret them in terms of a nonautonomous system of delay differential equations with a bounded additive perturbation. Second, by assessing the practical stability of this error system, conditions for practical partial synchronization are derived and formulated in terms of linear matrix inequalities. In addition, an explicit relation between the size of perturbation and the bound of the synchronization error is provided.

Original languageEnglish
Article number013126
Number of pages18
JournalChaos
Volume30
Issue number1
DOIs
Publication statusPublished - 16 Jan 2020

Funding

This work was supported by Project No. C14/17/072 of the KU Leuven Research Council, by Project No. G0A5317N of the Research Foundation-Flanders (FWO-Vlaanderen), and by Project UCoCoS funded by the European Unions Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement No. 675080.

FundersFunder number
Research Foundation Flanders
Research Foundation Flanders
European Union's Horizon 2020 - Research and Innovation Framework Programme
Katholieke Universiteit LeuvenG0A5317N
European Union's Horizon 2020 - Research and Innovation Framework Programme675080

    Fingerprint

    Dive into the research topics of 'Robust partial synchronization of delay-coupled networks'. Together they form a unique fingerprint.

    Cite this