  In a seminal article, Kahn has introduced the notion of process network and
given a semantics for those using Scott domains whose elements are (possibly
infinite) sequences of values. This model has since then become a standard tool
for studying distributed asynchronous computations. From the beginning, process
networks have been drawn as particular graphs, but this syntax is never
formalized. We take the opportunity to clarify it by giving a precise
definition of these graphs, that we call nets. The resulting category is shown
to be a fixpoint category, i.e. a cartesian category which is traced wrt the
monoidal structure given by the product, and interestingly this structure
characterizes the category: we show that it is the free fixpoint category
containing a given set of morphisms, thus providing a complete axiomatics that
models of process networks should satisfy. We then use these tools to build a
model of networks in which data vary over a continuous time, in order to
elaborate on the idea that process networks should also be able to encompass
computational models such as hybrid systems or electric circuits. We relate
this model to Kahn's semantics by introducing a third model of networks based
on non-standard analysis, whose elements form an internal complete partial
order for which many properties of standard domains can be reformulated. The
use of hyperreals in this model allows it to formally consider the notion of
infinitesimal, and thus to make a bridge between discrete and continuous time:
time is "discrete", but the duration between two instants is infinitesimal.
Finally, we give some examples of uses of the model by describing some networks
implementing common constructions in analysis.
