Bifurcations in a chaotic dynamical system

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but.committeeprof. RNDr. Josef Šlapal, CSc. (předseda) prof. RNDr. Miloslav Druckmüller, CSc. (místopředseda) doc. Ing. Luděk Nechvátal, Ph.D. (člen) doc. RNDr. Jiří Tomáš, Dr. (člen) doc. Ing. Jiří Šremr, Ph.D. (člen) Assoc. Prof. Massimiliano Giuli (člen)cs
but.defenceadditional question: Šlapal - what would be the defence against the bad reportcs
but.jazykangličtina (English)
but.programAplikované vědy v inženýrstvícs
but.resultpráce byla úspěšně obhájenacs
dc.contributor.advisorNechvátal, Luděken
dc.contributor.authorKateregga, George Williamen
dc.contributor.refereeTomášek, Petren
dc.date.created2019cs
dc.description.abstractDynamical 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.en
dc.description.abstractDynamical 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.cs
dc.description.markEcs
dc.identifier.citationKATEREGGA, G. Bifurcations in a chaotic dynamical system [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2019.cs
dc.identifier.other117088cs
dc.identifier.urihttp://hdl.handle.net/11012/175467
dc.language.isoencs
dc.publisherVysoké učení technické v Brně. Fakulta strojního inženýrstvícs
dc.rightsStandardní licenční smlouva - přístup k plnému textu bez omezenícs
dc.subjectDynamical Systemsen
dc.subjectBifurcationen
dc.subjectChaosen
dc.subjectattractoren
dc.subjectLyapunov exponenten
dc.subjectDynamical Systemscs
dc.subjectBifurcationcs
dc.subjectChaoscs
dc.subjectattractorcs
dc.subjectLyapunov exponentcs
dc.titleBifurcations in a chaotic dynamical systemen
dc.title.alternativeBifurcations in a chaotic dynamical systemcs
dc.typeTextcs
dc.type.drivermasterThesisen
dc.type.evskpdiplomová prácecs
dcterms.dateAccepted2019-06-11cs
dcterms.modified2019-09-24-11:58:52cs
eprints.affiliatedInstitution.facultyFakulta strojního inženýrstvícs
sync.item.dbid117088en
sync.item.dbtypeZPen
sync.item.insts2025.03.27 08:46:25en
sync.item.modts2025.01.15 22:35:18en
thesis.disciplineMatematické inženýrstvícs
thesis.grantorVysoké učení technické v Brně. Fakulta strojního inženýrství. Ústav matematikycs
thesis.levelInženýrskýcs
thesis.nameIng.cs
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