  Genetic regulatory networks are usually modeled by systems of coupled
differential equations and by finite state models, better known as logical
networks, are also used. In this paper we consider a class of models of
regulatory networks which present both discrete and continuous aspects. Our
models consist of a network of units, whose states are quantified by a
continuous real variable. The state of each unit in the network evolves
according to a contractive transformation chosen from a finite collection of
possible transformations, according to a rule which depends on the state of the
neighboring units. As a first approximation to the complete description of the
dynamics of this networks we focus on a global characteristic, the dynamical
complexity, related to the proliferation of distinguishable temporal behaviors.
In this work we give explicit conditions under which explicit relations between
the topological structure of the regulatory network, and the growth rate of the
dynamical complexity can be established. We illustrate our results by means of
some biologically motivated examples.
