  In this paper we develop a theory to describe innovation processes in a
network of interacting units. We introduce a stochastic picture that allows for
the clarification of the role of fluctuations for the survival of innovations
in such a non-linear system. We refer to the theory of complex networks and
introduce the notion of sensitive networks. Sensitive networks are networks in
which the introduction or the removal of a node/vertex dramatically changes the
dynamic structure of the system. As an application we consider interaction
networks of firms and technologies and describe technological innovation as a
specific dynamic process. Random graph theory, percolation, master equation
formalism and the theory of birth and death processes are the mathematical
instruments used in this paper.
