Modelling Selforganization and Innovation Processes in Networks

Details Modelling Selforganization and Innovation Processes in Networks Modelling Selforganization and Innovation Processes in Networks

2004-06-18

arxiv.org/abs/cond-mat/0406425v1

Physics

Condensed Matter

Statistical Mechanics

59 pages LaTeX, 15 figures (in part LaTeX generated), Springer LNP style

Scientific paper

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.

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