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Modelling Selforganization and Innovation Processes in Networks

Ingrid Hartmann-Sonntag·Andrea Scharnhorst·Werner Ebeling
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Abstract

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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Ingrid Hartmann-Sonntag, Andrea Scharnhorst, Werner Ebeling. 2004-06-18. Modelling Selforganization and Innovation Processes in Networks. https://arxiv.org/abs/cond-mat/0406425

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