state ($\tau_i$ for the $i$-th oscillator) defining its internal timer. Once the timer of any oscillator reaches a threshold (${\bar{\tau}}$), it triggers an impulse and is reset to zero. At such an event, all the other impulse-coupled oscillators rescale their timer by a factor given by $(1+ \varepsilon)$ times the value of their timer, where $\varepsilon \in (-1,0)$.[^2] Figure \[fig:example\] shows a trajectory of two impulse-coupled oscillators [with states]{} ${\tau_1}$ and ${\tau_2}$. In this figure, the dark red circles indicate when a timer state has reached the threshold and, thus, resets to zero. The light green circles indicate when an oscillator is externally reset and, hence, decreases its timer by $(1+\varepsilon)$ times its current state.

According to this outline of the model, the dynamics of the impulse-coupled oscillators involve impulses and timer resets, which are treated as true discrete events and instantaneous updates, while the smooth evolution of the timers before/after these events define the continuous dynamics. We follow the hybrid formalism of [@teel2012hybrid; @Goebel.ea.09.CSM], where a hybrid system is given by four objects $(C,f,D,G)$ defining its *data*:

-   *Flow set:* a set $C \subset {\mathbb{R}}^{N}$ specifying the points where flows are possible (or continuous evolution).

-   *Flow map:* a 