Pattern selection in a lattice of pulse-coupled oscillators

Abstract

We study spatio-temporal pattern formation in a ring of N oscillators with inhibitory unidirectional pulselike interactions. The attractors of the dynamics are limit cycles where each oscillator fires once and only once. Since some of these limit cycles lead to the same pattern, we introduce the concept of pattern degeneracy to take it into account. Moreover, we give a qualitative estimation of the volume of the basin of attraction of each pattern by means of some probabilistic arguments and pattern degeneracy, and show how are they modified as we change the value of the coupling strength. In the limit of small coupling, our estimative formula gives a perfect agreement with numerical simulations.