Pattern selection in a lattice of pulse-coupled oscillators

TL;DR

This paper investigates how spatio-temporal patterns form in a ring of pulse-coupled oscillators with inhibitory interactions, analyzing attractors, pattern degeneracy, and basin volumes as coupling varies.

Contribution

It introduces the concept of pattern degeneracy and provides a probabilistic estimation of basin volumes, validated by numerical simulations for small coupling.

Findings

Pattern degeneracy affects the number of distinct attractors.

The basin volume estimation matches simulations at small coupling.

Coupling strength influences pattern stability and basin sizes.

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.