Analýza charakteru pohybu Bělousovova–Žabotinského modelu v závislosti na parametru

The main aim of this thesis is to detect dynamical properties of the Györgyi-Field model of the Belousov-Zhabotinsky chemical reaction. The corresponding three-variable model given as a set of nonlinear ordinary differential equations depends on one parameter, the flow rate. As certain values of this parameter can give rise to chaos, the analysis was performed in order to identify different dynamics regimes. Dynamical properties were qualified and quantified using classical and also new techniques. Namely, phase portraits, bifurcation diagrams, the Fourier spectra analysis, the 0-1 test for chaos, and approximate entropy. The correlation between approximate entropy and the 0-1 test for chaos was observed and described in detail. Moreover, the three-stage system of nested subintervals of flow rates, for which in every level the 0-1 test for chaos and approximate entropy was computed, is showing the same pattern. The study leads to an open problem whether the set of flow rate parameters has Cantor like structure.Hlavním cílem této práce je zkoumat dynamické vlastnosti Györgyi-Fieldova modelu Belousov-Žabotinského chemické reakce. Odpovídající model o třech proměnných je zadaný soustavou nelineárních obyčejných diferenciálních rovnic závislých na jednom parametru, který označuje průtok. Protože některé hodnoty tohoto parametru mohou vést k chaosu, byla provedena analýza za účelem identifikace různých dynamických režimů. Dynamické vlastnosti byly kvalifikovány a kvantifikovány klasickými i novými technikami, jako jsou fázové portréty, bifurkační diagram, Fourierova spektrální analýza, 0-1 test na chaos a aproximační entropie. Podrobně byla zkoumána korelace mezi aproximační entropií a 0-1 testem chaosu. Navíc byl zkonstruován systém tří vnořených podintervalů parametru průtoků, pro který byl v každé úrovni vypočítán 0-1 test na chaos a aproximační entropie, které měly stejnou strukturu. Studie vede k otevřenému problému, zda množina parametrů průtoku má strukturu podobnou Cantorově množině.470 - Katedra aplikované matematikyvýborn

WOFEX 2021 : 19th annual workshop, Ostrava, 1th September 2021 : proceedings of papers

The workshop WOFEX 2021 (PhD workshop of Faculty of Electrical Engineer-ing and Computer Science) was held on September 1st September 2021 at the VSB – Technical University of Ostrava. The workshop offers an opportunity for students to meet and share their research experiences, to discover commonalities in research and studentship, and to foster a collaborative environment for joint problem solving. PhD students are encouraged to attend in order to ensure a broad, unconfined discussion. In that view, this workshop is intended for students and researchers of this faculty offering opportunities to meet new colleagues.Ostrav

Acceleration of time series entropy algorithms

This paper concentrates on the entropy estimation of time series. Two new algorithms are introduced: Fast Approximate Entropy and Fast Sample Entropy. Their main advantage is their lower time complexity. Examples considered in the paper include interesting experiments with real-world data obtained from IT4Innovations' supercomputers Salomon and Anselm, as well as with data artificially created specifically to test the credibility of these new entropy analyzers.Web of Science7531454144