Investigation of mathematical models stability and geometry configurations

The article discusses application of the theory of stability, previously developed for solving discrete optimization problems. The theory allows considering two types of the applied problems arising during a networks modelling. The modelled process P occurs in time and has several components K₁,...,K_s. Its mathematical models are presented as optimization problems, parametric programming problems or computational geometry problems Z₁,...,Z_s. A practical question arises if there is any relationship between the model and real process. The theory of stability is used in mathematical modelling because it allows linking various components of the process with the help of "uniform" formulae, algorithms and convincingly indicating "bottlenecks" of the model. While analyzing properties of the geometric configurations, the proposed approach allows identifying the "critical" situations. By virtue of parameterization, the input data can be presented as time functions. This allows considering the models of some processes under certain conditions as well as drawing heuristic conclusions about the compatibility of the model with the simulated process. The article describes a general scheme of analyzing the stability analysis problem. It shows the application of this scheme and gives examples illustrating its application.

References

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