Název: Bifurcations in a chaotic dynamical system
Překlad názvu: Bifurcations in a chaotic dynamical system
Autoři: Kateregga, George William ; Tomášek, Petr (oponent) ; Nechvátal, Luděk (vedoucí práce)
Typ dokumentu: Diplomové práce
Rok: 2019
Jazyk: eng
Nakladatel: Vysoké učení technické v Brně. Fakulta strojního inženýrství
Abstrakt: Dynamical systems possess an interesting and complex behaviour that have attracted a number of researchers across different fields, such as Biology, Economics and most importantly in Engineering. The complex and unpredictability of nonlinear customary behaviour or the chaotic behaviour, makes it strange to analyse them. This thesis presents the analysis of the system of nonlinear differential equations of the so--called Lu--Chen--Cheng system. The system has similar dynamical behaviour with the famous Lorenz system. The nature of equilibrium points and stability of the system is presented in the thesis. Examples of chaotic dynamical systems are presented in the theory. The thesis shows the dynamical structure of the Lu--Chen--Cheng system depending on the particular values of the system parameters and routes to chaos. This is done by both the qualitative and numerical techniques. The bifurcation diagrams of the Lu--Chen--Cheng system that indicate limit cycles and chaos as one parameter is varied are shown with the help of the largest Lyapunov exponent, which also confirms chaos in the system. It is found out that most of the system's equilibria are unstable especially for positive values of the parameters $a, b$. It is observed that the system is highly sensitive to initial conditions. This study is very important because, it supports the previous findings on chaotic behaviours of different dynamical systems.
Klíčová slova: attractor; Bifurcation; Chaos; Dynamical Systems; Lyapunov exponent; attractor; Bifurcation; Chaos; Dynamical Systems; Lyapunov exponent

Instituce: Vysoké učení technické v Brně (web)
Informace o dostupnosti dokumentu: Plný text je dostupný v Digitální knihovně VUT.
Původní záznam: http://hdl.handle.net/11012/175467

Trvalý odkaz NUŠL: http://www.nusl.cz/ntk/nusl-401527


Záznam je zařazen do těchto sbírek:
Školství > Veřejné vysoké školy > Vysoké učení technické v Brně
Vysokoškolské kvalifikační práce > Diplomové práce