Global analysis of pulse-coupled oscillators: discrete and continuous models

The Peskin model [1] is a simple but seminal model to study networks of interacting agents, such as pacemaker cells of the heart or neurons. Each agent corresponds to an oscillator whose state variable xi evolves according to the dynamics ẋi = F(xi) > 0 between two threshold values. Upon reaching the upper threshold, the state is reset to the lower threshold — the oscillator is said to fire. The coupling is defined as follows: whenever an oscillator fires, it emits a pulse which instantaneously increases by ε > 0 the state of every other oscillators.