Modelling Selforganization and Innovation Processes in Networks

TL;DR

This paper develops a stochastic theory for innovation in complex networks, highlighting the impact of fluctuations and the concept of sensitive networks where small changes drastically alter dynamics.

Contribution

It introduces a novel stochastic framework for modeling innovation processes and defines sensitive networks, applying mathematical tools like graph theory and percolation to analyze technological innovation.

Findings

Fluctuations influence innovation survival in networks.

Sensitive networks exhibit dramatic structural changes with node modifications.

Mathematical modeling captures dynamics of firm and technology interactions.

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.