We study systems of identical coupled oscillators introducing a distribution of delay times in the coupling. For arbitrary network topologies, we show that the frequency and stability of the fully synchronized states depend only on the mean of the de
lay distribution. However, synchronization dynamics is sensitive to the shape of the distribution. In the presence of coupling delays, the synchronization rate can be maximal for a specific value of the coupling strength.
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.
