\, w_p(t)=0} \dfrac{m_p(t)}{a^-_{qp}\tau_p} \, .$$ This equation also holds if $|q{^{\textrm{in}}}| = 1$ and if the upstream place of $q$ has a single output transition.

We respectively denote by $m(t)$, $w(t)$ and $f(t)$ the vectors of entries $m_p(t)$, $w_p(t)$ and $f_q(t)$.

Albeit the dynamics that we presented so far is piecewise affine, a trajectory $t \mapsto (m(t), w(t), f(t))$ may be discontinuous. Indeed, in , the set of the places over which the minimum is taken may change over time. If at time $t$, there is a new place $p \in q{^{\textrm{in}}}$ such that $w_p(t)$ cancels, and if the quantity ${m_p(t)}/(a^-_{qp}\tau_p)$ is sufficiently small, then the minimum in  (and subsequently the flow $f_q(t)$) discontinuously jumps to the latter value.

Initial conditions of the dynamics are specified by a pair $(m(t_i),w(t_i))$ such that the minimum in  makes sense, [*i.e.*]{}, at least one $w_p(t_i)$ is equal to $0$ for each set of places $q{^{\textrm{in}}}$. One can easily show that if the set $\{ p \in q{^{\textrm{in}}}\colon w_p(t) = 0\} $ is nonempty for all transition $q \in {\mathcal{Q}}$ at time $t = t_i$, then it remains nonempty for all time $t \geq t_i$.

The dynamics – may admit different trajectories for a 