# Regensburg 2019 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 8: Networks: From Topology to Dynamics (joint session DY/SOE)

### DY 8.10: Vortrag

### Montag, 1. April 2019, 17:30–17:45, H20

**Synchronization of time-varying networks with coupling delays** — •Otti D'Huys^{1}, Javier Rodríguez-Laguna^{2}, Manuel Jiménez-Martín^{2}, and Elka Korutcheva^{2} — ^{1}Department of Mathematics, Aston University, B4 7ET Birmingham, United Kingdom — ^{2}Departamento de Física Fundamental, UNED, Spain

We study the effect of a fluctuating topology in delay-coupled networks. Such network fluctuations are common, for instance, between interacting neurons, or networks modeling social interactions.

We concentrate on the synchronization properties of chaotic maps. The topology fluctuates between an ensemble of small-world networks. The dynamics is characterized by three timescales: the internal time scale of the node dynamics, the connection delay along the links, and the timescale of the network fluctuations. When the network fluctuations are faster than the coupling delay and the internal time scale, the synchronized state can be stabilized by the fluctuations. As the network time scale increases, the synchronized state becomes unstable when both time scales collide.

We complement these results with an analytical theory in the linearized limit. Two limit cases allow an interpretation in terms of an `effective network': When the network fluctuations are much faster than the internal time scale and the coupling delay, the effective network topology is the average over the different topologies. When coupling delay and network fluctuation time scales collide, the effective topology is the geometric mean over the different topologies.