Travelling waves in chains of pulse-coupled integrate-and-fire oscillatorswith 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 latt er 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 freque ncies across the chain and the form of delayed interactions. A linear stabi lity analysis of phase-locked solutions is carried out in terms of perturba tions of the firing times of the oscillators. it is shown how travelling wa ves destabilize when the detuning between oscillators or the strength of th e coupling becomes too large. (C)1999 Elsevier Science B.V. All rights rese rved.