Summary
International Symposium on Nonlinear Theory and its Applications
2010
Session Number:A2L-A
Session:
Number:A2L-A1
Generalized modeling of heterogeneous nonlinear networks
Thilo Gross, Dirk Stiefs, Lars Rudolf, Martin Zumsande,
pp.75-78
Publication Date:2010/9/5
Online ISSN:2188-5079
Summary:
Generalized modeling (GM) can be used to explore the dynamics of large, complex networks of nonlinear dynamical elements. Importantly, the interaction terms in the corresponding dynamical systems do not need to be fixed but can be expressed as general (i.e., unspecified) functions, describing a large class of different conventionalmodels. A normalization procedure is then used to derive the Jacobian matrix governing the dynamics close to all steady states in the whole class of models. By GM the Jacobian matrices can be expressed as functions of parameters that have a well defined interpretation in the context of the respective application. By an ecological example, we show how GM can be used to obtain meaningful information on the dynamics on networks comprising 50 variables and thousands of parameters.