2004/06/18 by Ingrid Hartmann-Sonntag, Hartmann-Sonntag, Ingrid, Andrea Scharnhorst +3
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Biological sciences #FOS: Physical sciences #Physics and Society (physics.soc-ph) #Populations and Evolution (q-bio.PE) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.dis-nn #cond-mat.stat-mech #nlin.AO #physics.soc-ph #q-bio.PE
paper · pdf · doi:10.48550/arxiv.cond-mat/0406425
59 pages LaTeX, 15 figures (in part LaTeX generated), Springer LNP style
arxiv created 2004/06/18 · arxiv updated 2009/12/01
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.