Collective modes of coupled phase oscillators with delayed coupling

TL;DR

This paper investigates how delayed coupling influences pattern formation and collective modes in spatially extended oscillator systems, with applications to biological segmentation clocks.

Contribution

It derives a continuum theory for collective modes in delayed coupled oscillators and applies it to biological systems, revealing delay-dependent phase profiles.

Findings

Delay affects phase profiles of collective modes.

Wave patterns depend on coupling delays and boundary conditions.

The theory explains biological patterning phenomena.

Abstract

We study the effects of delayed coupling on timing and pattern formation in spatially extended systems of dynamic oscillators. Starting from a discrete lattice of coupled oscillators, we derive a generic continuum theory for collective modes of long wavelength. We use this approach to study spatial phase profiles of cellular oscillators in the segmentation clock, a dynamic patterning system of vertebrate embryos. Collective wave patterns result from the interplay of coupling delays and moving boundary conditions. We show that the phase profiles of collective modes depend on coupling delays.