# Dresden 2011 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 14: Delay Dynamics

### DY 14.4: Vortrag

### Dienstag, 15. März 2011, 14:45–15:00, ZEU 255

**Effect of distributed delays on synchronization dynamics** — •Lucas Wetzel^{1}, Saul Ares^{1}, Luis G. Morelli^{2}, Andrew C. Oates^{2}, and Frank Jülicher^{1} — ^{1}Max Planck Institute for the Physics of Complex Systems, Dresden — ^{2}Max Planck Institute of Molecular Cell Biology and Genetics, Dresden

We study systems of identical coupled phase oscillators, introducing a delay distribution that weights the contributions to the coupling arising from different past times. We have previously shown that for an arbitrary coupling topology with equal number of neighbors for each oscillator, the frequency and stability of the fully synchronized states only depend on the first moment of the delay distribution.

In this contribution we will explore the dynamics of systems approaching full synchronization. We find analytical expressions, confirmed through numerical simulations, for the exponential decay of small perturbations and the dependence of this decay on the delay distribution. We conclude that distributed delays can change the transient behavior for systems with nearest neighbor coupling, but not in the case of mean field. This result may be relevant to biological systems, where fluctuations in the frequency of individual oscillators keep the system away from the synchronized state, and coupling is required to counteract such fluctuations.