Understanding the enhanced synchronization of delay-coupled networks with fluctuating topology

Otti D'Huys, Javier Rodríguez-Laguna, Manuel Jiménez-Martín, Elka Korutcheva, Wolfgang Kinzel

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We study the dynamics of networks with coupling delay, from which the connectivity changes over time. The synchronization properties are shown to depend on the interplay of three time scales: the internal time scale of the dynamics, the coupling delay along the network links and time scale at which the topology changes. Concentrating on a linearized model, we develop an analytical theory for the stability of a synchronized solution. In two limit cases the system can be reduced to an “effective” topology: In the fast switching approximation, when the network fluctuations are much faster than the internal time scale and the coupling delay, the effective network topology is the arithmetic mean over the different topologies. In the slow network limit, when the network fluctuation time scale is equal to the coupling delay, the effective adjacency matrix is the geometric mean over the adjacency matrices of the different topologies. In the intermediate regime the system shows a sensitive dependence on the ratio of time scales, and specific topologies, reproduced as well by numerical simulations. Our results are shown to describe the synchronization properties of fluctuating networks of delay-coupled chaotic maps.
Original languageEnglish
Pages (from-to)1129–1150
JournalThe European Physical Journal: Special Topics
Issue number10-11
Publication statusPublished - 12 Dec 2018

Bibliographical note

© The Author(s) 2018. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://doi.org/creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Funding: O.D. has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 713694 (MULTIPLY). This work was partly supported by the Spanish Government through grant FIS-2015-69617-C2-1-P (J.R.-L.) and the Alexander von Humboldt Foundation within the Renewed research stay program (E.K.).


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