Dresden 2009 – wissenschaftliches Programm

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AGSOE: Arbeitsgruppe Physik sozio-ökonomischer Systeme

AGSOE 18: Networks: From Topology to Dynamics III

AGSOE 18.2: Vortrag

Donnerstag, 26. März 2009, 14:30–15:00, BAR 205

Extracting Dynamics from System Topology by Generalized Modeling — •Thilo Gross — Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, 01187 Dresden

In several disciplines, ranging from biology to sociology and psychology, the topology of the network of interactions between system components is often either clear or suspected. By contrast the dynamical laws governing the interplay between these components are hard to derive, prohibiting a detailed mathematical analysis. For instance in ecology it is often known who-eats-who, but it is difficult to restrict these interactions to specific mathematical functions and parameter values. Therefore the term model is often used to refer to a diagrammatic representation of a system rather than a set of equations. In this talk I will show how generalized modeling can be used to investigate the local dynamics around all steady states of all potential systems of differential equations that are consistent with a given diagrammatic representations. In this way we can: identify important parameters for the local dynamical stability of the system; identify bifurcation points at which the stability is lost; and draw further conclusions on local and global dynamics from bifurcation analysis. The numerical performance of generalized models is so favorable that it can be used to statistically explore systems with thousands of unknown parameters. The approach will be illustrated by several examples from psychology and sociology.