FEDORKOVÁ, L. Metody stabilizace nestabilních řešení diskrétní logistické rovnice [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2019.
This thesis deals with stability analysis of the controlled discrete logistic map. Three types of a feedback controller are applied to this classical discrete model that displays a very rich qualitative behaviour of solutions. The main issue connected with implementation of these controllers is connected with stabilization of unstable steady states and periodic orbits of higher orders of this model (some questions related to chaos control are discussed as well). The topic of this thesis has been discussed in several existing papers whose results are often based rather on numerical experiments that on a theoretical justification. Therefore, this topic has offered two possibilities how to contribute to existing results. Firstly, to perform a survey of these results supported by various comparisons of the used control methods with respect to different viewpoints. Secondly, to make a theoretical contribution to the current research in this area. In my opinion, the authoress succeeded in both these aspects. She managed to make a very comprehansive survey of stabilization methods for discrete dynamical systems, including discussions of their properties. Also, the work involves a theoretical justification and computation of a certain bifurcation value whose existence has been observed only numerically so far. Finally, I would like to express my contentment with activity and responsibility of the authoress during preparation of this work. For the above reasons, I recommend this thesis to the final defence.
| Kritérium | Známka | Body | Slovní hodnocení |
|---|---|---|---|
| Splnění požadavků a cílů zadání | A | ||
| Postup a rozsah řešení, adekvátnost použitých metod | A | ||
| Vlastní přínos a originalita | A | ||
| Schopnost interpretovat dosažené výsledky a vyvozovat z nich závěry | A | ||
| Využitelnost výsledků v praxi nebo teorii | A | ||
| Logické uspořádání práce a formální náležitosti | B | ||
| Grafická, stylistická úprava a pravopis | B | ||
| Práce s literaturou včetně citací | A | ||
| Samostatnost studenta při zpracování tématu | A |
The thesis deals with several approaches of solution stabilization applied to the logistic equation. The analysis presented in the thesis is remarkably detailed and conclusions are clearly formulated . The analysis is supported by appropriate graphical outputs. Several figures have too tiny captions and legend (see e.g. figure groups at pages 60 - 64). There is only a few factual errors and grammar mistakes in the thesis, e.g. p. 23, line 14: At the gain K(y(n-1)) in N x R^m to R^(m x m), there should be just R^m to R^(m x m) (without “N x”). several times a verb “setted” occurs in the theses, which is not correct gramatical form of the verb “set”. The thesis comes also with a new qualitative result – a critical value of bifurcation parameter (in the case of DFC approach) is derived via solution of the fourth order algebraic equation. The overall impression of the thesis is great, thence my assessment is A/excellent.
| Kritérium | Známka | Body | Slovní hodnocení |
|---|---|---|---|
| Splnění požadavků a cílů zadání | A | ||
| Postup a rozsah řešení, adekvátnost použitých metod | A | ||
| Vlastní přínos a originalita | A | ||
| Schopnost interpretovat dosaž. výsledky a vyvozovat z nich závěry | A | ||
| Využitelnost výsledků v praxi nebo teorii | A | ||
| Logické uspořádání práce a formální náležitosti | A | ||
| Grafická, stylistická úprava a pravopis | B | ||
| Práce s literaturou včetně citací | A |
eVSKP id 113124