hence summarizes the three possible place/transition patterns that can occur in this class of Petri nets.

![Conflict, synchronization and priority patterns[]{data-label="fig:configuration"}](main-FINAL-figure0.pdf)

Continuous dynamics and routing rules
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We now equip the Petri net with a continuous semantics. Given a transition $q$, we associate a flow $f_q(t)$ which represents the instantaneous firing rate of transition $q$ at time $t$. We also associate with each place $p$ a [*marking*]{} $M_p(t)$, which is a continuous real valued function of the time $t$. In the case of [*discrete*]{} timed Petri nets, one typically requires that every token stays a minimum time in the place, — at this stage, the token may be considered as [*under processing*]{} — before becoming available for the firing of output transitions. To capture this property in the continuous setting, we assume that the marking $M_p(t)$ can be decomposed as $M_p(t)=m_p(t)+w_p(t)$, where $m_p(t)$ is the quantity of tokens under processing and $w_p(t)$ is the quantity of tokens waiting to contribute to the firing of an output transition.

We associate with each place $p$ a time constant $\tau_p>0$. Each token entering in a place is processed with the rate $1/\tau_p$. This leads to the following differential equation: $$\label{eq:mp}
  \dot{m}_p(t) = \sum_{q 