Pattern selection in a lattice of pulse-coupled oscillators

We study spatio-temporal pattern formation in a ring of N oscillators with inhibitory unidirectional pulselike interactions. The attractors of the dyn amics are limit cycles where each oscillator fires once and only once. Sinc e some of these limit cycles lead to the same pattern, we introduce the con cept of pattern degeneracy to take it into account. Moreover, we give a qua litative estimation of the volume of the basin of attraction of each patter n by means of some probabilistic arguments and pattern degeneracy, and show how they are modified as we change the value of the coupling strength. In the limit of small coupling, our estimative formula gives a pefect agreemen t with numerical simulations. [S1063-651X(99)02110-8].