Generalized models as an universal approach to the analysis of nonlinear dynamical systems

Thilo Gross, Ulrike Feudel

Research output: Contribution to journalArticle (Academic Journal)peer-review

89 Citations (Scopus)


We present a universal approach to the investigation of the dynamics in generalized models. In these models the processes that are taken into account are not restricted to specific functional forms. Therefore a single generalized models can describe a class of systems which share a similar structure. Despite this generality, the proposed approach allows us to study the dynamical properties of generalized models efficiently in the framework of local bifurcation theory. The approach is based on a normalization procedure that is used to identify natural parameters of the system. The Jacobian in a steady state is then derived as a function of these parameters. The analytical computation of local bifurcations using computer algebra reveals conditions for the local asymptotic stability of steady states and provides certain insights on the global dynamics of the system. The proposed approach yields a close connection between modelling and nonlinear dynamics. We illustrate the investigation of generalized models by considering examples from three different disciplines of science: a socio-economic model of dynastic cycles in china, a model for a coupled laser system and a general ecological food web.
Original languageEnglish
Article number016205
Number of pages14
JournalPhysical Review E: Statistical, Nonlinear, and Soft Matter Physics
Publication statusPublished - 2006

Structured keywords

  • Engineering Mathematics Research Group


Dive into the research topics of 'Generalized models as an universal approach to the analysis of nonlinear dynamical systems'. Together they form a unique fingerprint.

Cite this