  Biological networks have been recently found to exhibit many topological
properties of the so-called complex networks. It has been reported that they
are, in general, both highly skewed and directed. In this paper, we report on
the dynamics of a Michaelis-Menten like model when the topological features of
the underlying network resemble those of real biological networks.
Specifically, instead of using a random graph topology, we deal with a complex
heterogeneous network characterized by a power-law degree distribution coupled
to a continuous dynamics for each network's component. The dynamics of the
model is very rich and stationary, periodic and chaotic states are observed
upon variation of the model's parameters. We characterize these states
numerically and report on several quantities such as the system's phase diagram
and size distributions of clusters of stationary, periodic and chaotic nodes.
The results are discussed in view of recent debate about the ubiquity of
complex networks in nature and on the basis of several biological processes
that can be well described by the dynamics studied.
