# Regensburg 2010 – wissenschaftliches Programm

## Bereiche | Tage | Auswahl | Suche | Downloads | Hilfe

# DY: Fachverband Dynamik und Statistische Physik

## DY 10: Nonlinear Dynamics I

### DY 10.2: Vortrag

### Dienstag, 23. März 2010, 14:15–14:30, H46

**Distributed vs Fixed Delay in a System of Coupled Phase Oscillators** — •Lucas Wetzel^{1}, Saúl Ares^{1}, Luis G. Morelli^{2}, Andrew C. Oates^{2}, and Frank Jülicher^{1} — ^{1}Max Planck Institute for the Physics of Complex Systems — ^{2}Max Planck Institute of Molecular Cell Biology and Genetics

Systems of coupled oscillators with delay in the coupling are important for several physical, chemical, engineering, and biological phenomena. In cellular systems, such as the vertebrate segmentation clock, fluctuations in gene expression and transport of macromolecules introduce a variability in the time delay associated with cell to cell communication. In order to account for such variability, we consider the effects of distributed delays.

We study systems of phase oscillators with different coupling topologies, introducing a delay distribution that describes the contributions to the coupling arising from different past times. Surprisingly, our calculations show that for an arbitrary coupling topology where each oscillator is identical and coupled to the same number of oscillators within the system, the frequency of the fully synchronized states as well as the stability of such solutions only depend on the first moment of the distribution. The system is thus closely related to one with a fixed delay whose value equals the first moment of the distribution.