Synchronization in Dynamical Systems Coupled via Multiple Directed Networks

We study synchronization and consensus in a group of dynamical systems coupled via multiple directed networks. We show that even though the coupling in a single network may not be sufficient to synchronize the systems, combination of multiple networks can contribute to synchronization. We illustrate...

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Bibliographic Details
Published inIEEE transactions on circuits and systems. II, Express briefs Vol. 68; no. 5; pp. 1660 - 1664
Main Author Wu, Chai Wah
Format Journal Article
LanguageEnglish
Published New York IEEE 01.05.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Coupling
Couplings
Directed graphs
Dynamical systems
Eigenvalues and eigenfunctions
Graph theory
Laplace equations
Networks
Nonlinear dynamical systems
Polytrees
Symmetric matrices
Synchronism
Synchronization
System effectiveness
Topology
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Summary:We study synchronization and consensus in a group of dynamical systems coupled via multiple directed networks. We show that even though the coupling in a single network may not be sufficient to synchronize the systems, combination of multiple networks can contribute to synchronization. We illustrate how the effectiveness of a collection of networks to synchronize the coupled systems depends on the graph topology. In particular, we show that if the graph sum is a directed graph whose reversal contains a spanning directed tree, then the network synchronizes if the coupling is strong enough. This is intuitive as there is a root node that influence every other node via a set of edges where each edge in the set is in one of the networks.
ISSN:1549-7747
1558-3791
DOI:10.1109/TCSII.2021.3068202