Dresden 2009 – wissenschaftliches Programm
DY 27.16: Poster
Donnerstag, 26. März 2009, 16:00–18:00, P1B
Time delay and noise in the Kuramoto model of coupled oscillators — •Lucas Wetzel1, Saul Ares1, Andrew C. Oates2, and Frank Julicher1 — 1Max Planck Institute for the Physics of Complex Systems — 2Max Planck Institute of Molecular Cell Biology and Genetics
Systems of coupled oscillators are important in several physical, chemical, engineering, and biological phenomena. Traditionally the coupling between different oscillators was assumed to be instantaneous, neglecting the time necessary for information flow between different oscillators. Time delays in the coupling affect fundamental properties of the system, like synchronization or the collective period of oscillators. However, little is known of the joint effect of noise and time delay. The noise can come from a distribution of the intrinsic frequencies of the oscillators, from a dynamical noise affecting the oscillators, or from stochastic variations of the time delays in the coupling. The latter case can be described by a distributed delay, where time delays are no longer given by a single number, but by a distribution over past times affecting the rate of oscillation in the present.
In this contribution we study the Kuramoto model of phase oscillators as a representative of systems of coupled oscillators. We introduce time delay in the coupling and characterize its effects in the presence of noise. Together with the basic understanding of the problem, we are motivated by the study of genetic oscillations in vertebrate segmentation, where a description based on phase oscillators has shown to be a valuable tool.