KHŮLOVÁ, J. Stabilita a chaos v nelineárních dynamických systémech [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2018.

Posudek vedoucího

Čermák, Jan

This thesis deals with analysis of basic chaotic dynamical systems, with a particular attention paid to the Rössler model. Besides the classical description of its route from stability to chaos, some related issues concerning stabilization and synchronization of this system are discussed, theoretically solved and numerically confirmed. The topic of this thesis provided an uneasy task. On the one hand, it required the knowledge of a theoretical background on chaotic dynamical systems and time-delay systems. On the other hand, a considerable programming skill was necessary in creation of various bifurcation diagrams and other numerical experiments illustrating theoretical conclusions. In my opinion, the authoress succeeded in both these aspects. She managed not only to study existing theoretical apparatus, but also extend it. In particular, results on stability of linear time-delay dynamical systems represent a novel contribution to this area. Presented applications of stability results to investigated stabilization and synchronization problems follow recent trends in these areas and provide various inspirations for a next research. Also, I would like to express my contentment with activity, responsibility and interest of the authoress during preparation of this work. Some minor inaccuracies appearing in the text has no substantial impact on its quality. For the above reasons, I recommend this thesis to the final defence.

Posudek oponenta

Tomášek, Petr

The thesis deals with nonlinear dynamical systems with an emphasis on chaos and related topics. After the brief introduction to dynamical systems theory the student presented a survey of several applications where chaotic behaviour can be observed. A special attention is paid to chaos control and synchronization processes. Both topics are illustrated on the Rössler system under various assumptions on the system parameters and initial conditions. The sources are properly cited and they appropriately supply the introduced considerations. There is a few minor typographical, grammar and a very few fact errors in the thesis, e.g. in czech extended abstract: "parametrů a,bq,c" - should be "parametrů a,b,c"; p. 18. There should be interval [t[0]-a,t[0]+a] instead of [-a,a] at the end of Theorem 3; p. 21. There is an extra symbol "l" within matrix H_n. p. 28. There is missing a predicate in the second sentence of section 2.4. p. 52. There should be minus sign instead of plus in the first row of the first equation: "s+K exp(-tau s)=s+K exp(-tau s)exp(i pi)" - should be "s+K exp(-tau s)=s-K exp(-tau s)exp(i pi)". The thesis gives a good introduction to chaos generating dynamical systems. Some techniques connected with their control (especially, time-delayed feedback control) and synchronization are introduced and applied to the Rössler system to demonstrate their applicability and efficiency. The presented analysis, considerations and conclusions are correct and an overall impression of the thesis is very positive. Thence my final assessment of the thesis is A/excellent.

eVSKP id 109332