Dresden 2009 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 4: Statistical physics in biological systems II (joint session DY/BP)
DY 4.8: Vortrag
Montag, 23. März 2009, 16:15–16:30, HÜL 386
Continuum limit of phase oscillators with delayed coupling — •Luis G. Morelli1,2, Saúl Ares1, Andrew C. Oates3, and Frank Jülicher1 — 1Max Planck Institute for the Physics of Complex Systems — 2Departamento de Física, Universidad de Buenos Aires, Buenos Aires, Argentina — 3Max Planck Institute of Molecular Cell Biology and Genetics
Complex oscillatory systems can sometimes be described as coupled phase oscillators. Time delays can be present in the coupling when the signal propagation velocity is finite or the signals are produced and processed through many step processes. It has been shown that delayed coupling can have important and non-trivial effects on collective dynamics, affecting the collective frequency and leading to complex regimes in which multiple stable frequencies can coexist. In this contribution we consider an extended system of coupled phase oscillators with time delays in the coupling. We develop a continuum description of the system for arbitrary values of the delay and obtain an effective phase diffusion equation. Delayed coupling introduces a frequency and coupling strength renormalization in the phase diffusion equation describing the continuum oscillatory media. The solutions to the phase diffusion equation show that the effects of delayed coupling can be important both for the temporal organization of the system as for the emergent spatial patterns of oscillation. We expect that our results will be useful in a wide range of problems in which time delays are significant for the collective dynamics.