Original title: Bifurcations in a chaotic dynamical system
Translated title: Bifurcations in a chaotic dynamical system
Authors: Kateregga, George William ; Tomášek, Petr (referee) ; Nechvátal, Luděk (advisor)
Document type: Master’s theses
Year: 2019
Language: eng
Publisher: Vysoké učení technické v Brně. Fakulta strojního inženýrství
Abstract: 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.
Keywords: attractor; Bifurcation; Chaos; Dynamical Systems; Lyapunov exponent; attractor; Bifurcation; Chaos; Dynamical Systems; Lyapunov exponent

Institution: Brno University of Technology (web)
Document availability information: Fulltext is available in the Brno University of Technology Digital Library.
Original record: http://hdl.handle.net/11012/175467

Permalink: http://www.nusl.cz/ntk/nusl-401527


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Universities and colleges > Public universities > Brno University of Technology
Academic theses (ETDs) > Master’s theses