2002 г., Том 7, Спец. выпуск, с.78-86

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 optimize a nonlinear time-discrete model. The ideas of Brayton and Tong are used to analyze a special representation of a nonlinear system which might be presented in that article. The underlying theory of the algorithm bases on the use of polytopes and linear programming techniques in such a way that in the course of iteration 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.
With this criterion 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 CO₂-simulations in the atmosphere is given.
As our basic motivation and application, we present the Technology-Emissions-Means-(TEM)-model, which is able to simulate a Joint Implementation Program. The approach underlines the importance of discrete mathematical methods in the field of system theory and ecological application. We consider structural frontiers from both the mathematical and applied viewpoints.