to zero only when all other states are less than that threshold; otherwise, if multiple timers reach the threshold simultaneously, the jump map is set valued to indicate that either $g_i(\tau) = 0$ or $g_i(\tau) = (1+\varepsilon)\tau_{i}$ is possible. This is to ensure that the jump map satisfies the regularity conditions outlined in Section \[sec:ModelForAnalysis\].[^3]

For example, consider the case $N=2$ the hybrid system ${{{\mathcal}H}}_N = (C,f,D,G)$ has state given by $$\tau=\left[ \begin{array}{c} \tau_{1} \\ \tau_{2}\end{array} \right] \in P_2 := [0,{\bar{\tau}}]\times[0,{\bar{\tau}}] .$$ The states $\tau_{1}$ and $\tau_{2}$ are the timers for both of the oscillators. The hybrid system ${{{\mathcal}H}}_2$ has the following data:

$${{{\mathcal}H}}_2 = \left\{\begin{array}{ll} C = P_2, & \qquad f(\tau) = \left[ \begin{array}{c} 1
\\ 1 \end{array}\right] \forall \tau \in C, \\ \noalign{\medskip} 
D = \left\{ \tau \in P_2 \ : \ \exists i \in \{1,2\} \ s.t. \ \tau_{i} = {\bar{\tau}}\right\}, & \qquad
G(\tau) = \left[ \begin{array}{c} g_1(\tau) \\ g_2(\tau) \end{array} \right] \forall \tau \in D , \end{array} \right.$$ where the functions $g_1$ and $g_2$ are defined as $$g_1 (\tau) = \left\{ \begin{array}{ll}  0 & \mbox{if } \tau_{1} = {\bar{\tau}}, \tau_2 < {\bar{\tau}}\\ \{0 , \tau_{1}(1+\varepsilon) \} & \mbox{if } \tau_{1} = {\bar{\tau}}, \tau_2 = {\bar{\tau}}\\
(1+\varepsilon)\tau_{1} 