Publications in Scientific Journals:
Ch. Kuehn, S. Siegmund, T. Gross:
"Dynamical analysis of evolution equations in generalized models";
IMA Journal of Applied Mathematics,
78
(2013),
5;
1051
- 1077.
English abstract:
Generalized models provide a framework for the study of evolution equations without specifying all
functional forms in the defining vector field. The generalized formulation of problems has been shown
to facilitate the analytical investigation of local dynamics and has been used successfully to answer
applied questions. Yet their potential to facilitate analytical computations has not been realized in the
mathematical literature. In the present paper, we introduce the method of generalized modelling in
mathematical terms, supporting the key steps of the procedure by rigorous proofs. Further, we point
out open questions that are in the scope of present mathematical research and if answered could greatly
increase the predictive power of generalized models.
Keywords:
generalized models, evolution equations, bifurcations, scaling transformation
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1093/imamat/hxs008
Created from the Publication Database of the Vienna University of Technology.