Travelling waves in chains of pulse-coupled integrate-and-fire oscillators with distributed delays

We analyse travelling waves in a chain of pulse-coupled integrate-and-fire oscillators with nearest-neighbour coupling and delayed interactions. This is achieved by approximating the equations for phase-locking in terms of a singularly perturbed two-point (continuum) boundary value problem. The latter has a solution provided that a self-consistent value for the collective frequency of oscillations can be found. We investigate how the qualitative behaviour of travelling waves depends on the distribution of natural frequencies across the chain and the form of delayed interactions. A linear stability analysis of phase-locked solutions is carried out in terms of perturbations of the firing times of the oscillators. it is shown how travelling waves destabilize when the detuning between oscillators or the strength of the coupling becomes too large. (C)1999 Elsevier Science B.V. All rights reserved.