Abstract
According to the approach of Brayton and Tong, a special representation form of polytopes may be used to construct an algorithm which is able to analyze and optimize a nonlinear time-discrete model. The ideas of Brayton and Tong will be presented. The underlying theory of the algorithm bases on the use of polytopes and linear programming techniques in such a way that in the successive proceeding only the extremal points of the polytopes have to be regarded. Their topological behavior can be used to get a stopping criterion which bases on transversality theory and methods of discrete mathematics. This is a new approach. With this criteria it is possible to state whether a given set of matrices determining our dynamical system, is stable or not.
Furthermore a new application in the field of CO 2-simulations in the atmosphere is given. We present the Technology-Emissions-Means- (TEM)-model, which is able to simulate a Joint Implementation Program.
Using symmetry properties it is possible to improve the algorithm. The presented results underline the importance of discrete mathematical methods in the field of system theory and ecological application.
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© 2003 Deutscher Universitäts-Verlag/GWV Fachverlage GmbH, Wiesbaden
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Pickl, S. (2003). Polytopes — Symmetries and Order of Extremal Points for Detecting Stability Regions of Time-Discrete Systems. In: Habenicht, W., Scheubrein, B., Scheubrein, R. (eds) Multi-Criteria- und Fuzzy-Systeme in Theorie und Praxis. Deutscher Universitätsverlag. https://doi.org/10.1007/978-3-322-81539-2_2
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DOI: https://doi.org/10.1007/978-3-322-81539-2_2
Publisher Name: Deutscher Universitätsverlag
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