Collective modes of coupled phase oscillators with delayed coupling

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.

arXiv comment5 pages, 2 figures

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Cited by in corpus (10)

• The Kuramoto model in complex networks
• Delay Regulated Explosive Synchronization in Multiplex Networks
• Synchronization Dynamics in the Presence of Coupling Delays and Phase Shifts
• Sequential pattern formation governed by signaling gradients
• Chemical event chain model of coupled genetic oscillators
• Nonequilibrium criticality driven by Kardar-Parisi-Zhang fluctuations in the synchronization of oscillator lattices
• Mobility-induced persistent chimera states
• Nonlinear transient waves in coupled phase oscillators with inertia
• The effect of distributed time-delays on the synchronization of neuronal networks
• Morphogen-regulated contact-mediated signaling between cells can drive the transitions underlying body segmentation in vertebrates