flow map $f$, there exist sets in the form of “lines" $\ell_k$, each of them in the direction ${\mathbf 1}$, which is the direction of the flow map, intersecting the jump set at a point which, for the $k$-th line, we denote as ${\widetilde}\tau^{k}$. We define the desynchronization set as the union of sets $\ell_{k}$ collecting points $\tau = {\widetilde}\tau^k + {\mathbf 1}s \in P_N$ parameterized by $s \in {\mathbb{R}}$.

To identify ${\widetilde}\tau^k$, consider a point ${\widetilde}\tau^{k} \in D\setminus {\mathcal{X}}$ with components satisfying ${\widetilde}\tau_{1}^{k} = {\bar{\tau}}> {\widetilde}\tau_{2}^{k} > {\widetilde}\tau_{3}^{k} > ... > {\widetilde}\tau_{N}^{k}$. Due to Definition \[def:desynch\], it must be true that the difference between jump times are constant. This means that there must be some correlation between $\Delta$ and the difference between, in this case, $\tau_{1}^{k}$ and $\tau_{2}^{k}$. Moreover, there must be a correlation between $\tau_{1}^{k}$ and all other states at jumps. It follows that this point belongs to ${\mathcal{A}}$ only if the distance between the expiring timer (${\widetilde}\tau_{1}^{k}$) and each of its other components (${\widetilde}\tau_{i}^{k}$, $i \in I \setminus \{1\}$) is equal to the distance between the value after the jump of the timer expiring next (${\widetilde}\tau_{2}^{k}\null^{+}$) and the value after the jump of its other components (${\widetilde}\tau_{i}^{k}\null^{+}$, 