Understanding the enhanced synchronization of delay-coupled networks with fluctuating topology
Department of Mathematics, Aston University,
B4 7ET Birmingham, UK
2 Departamento de Física Fundamental, UNED, 28040 Madrid, Spain
3 G. Nadjakov Inst. Solid State Physics, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria
4 Institut für theoretische Physik, Universität Würzburg, Am Hubland, 97072 Würzburg, Germany
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Received in final form: 6 July 2018
Published online: 12 December 2018
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 on the 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.
© The Author(s) 2018
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