Analysis in Pulse-Coupled Oscillators with Symmetry

Abstract

Synchronization in biological systems, such as synchronized luminosity of fireflies and synchronization of cardiac cells, is realized by interactions among oscillators with pulse signals. These systems with pulse signal couplings are called pulse-coupled oscillators. This paper analyses the synchronization of bi-directional pulse-coupled oscillators. Extending an analysis method of ring arrayed uni-directional pulse-coupled oscillators with the integrate-and-fire model, we show various synchronization patterns in bi-directional coupling oscillators, and analyze their stabilities. Moreover, numerical simulation shows the relationships between the spacial symmetry of the system and synchronization patterns.