delo diplomskega seminarja
Tadej Meglić (Author), Jasna Prezelj-Perman (Mentor)

Abstract

Majhna sprememba v začetnem stanju sistema privede do dolgoročno velikih sprememb. Ta lastnost oteži analizo raznih dinamičnih sistemov, kar nam predstavlja velik problem, saj je resnično življenje večinoma sestavljeno iz takšnih situacij. Kljub temu bomo z raznimi orodji poiskali zanimive rezultate o nepredvidljivem Lorenzovem sistemu. Videli bomo, kdaj se začne obnašati kaotično. S pomočjo Hartman- Grobmanovega izreka ga bomo linearizirali ter s tem poenostavili lokalno analizo kvalitativnih lastnosti. Uporabili bomo funkcijo Ljapunova, s katero bomo globalno preučili, kam gredo rešitve pri določenih parametrih.

Keywords

kaos;dinamični sistemi;diferencialne enačbe;bifurkacije;

Data

Language: Slovenian
Year of publishing:
Typology: 2.11 - Undergraduate Thesis
Organization: UL FMF - Faculty of Mathematics and Physics
Publisher: [T. Meglić]
UDC: 517.9
COBISS: 58558979 Link will open in a new window
Views: 1909
Downloads: 188
Average score: 0 (0 votes)
Metadata: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

Other data

Secondary language: English
Secondary title: Butterfly effect
Secondary abstract: Small changes in the initial state of the system can cause massive changes in the long run. This causes the analysis of said dynamical system significantly more difficult, which poses a problem, as situations of this sort arise in many fields of science. Nevertheless, we will find interesting results about the unexpected behaviour of Lorenz system. We will see at which parameters it behaves chaotically. Using the Hartman-Grobman theorem, we will linearize the system, making it easier to analyze locally. We will be using a Liapunov function to globally analyse the behaviour of solutions at certain parameters.
Secondary keywords: chaos;dynamical systems;differential equations;bifurcation;
Type (COBISS): Final seminar paper
Study programme: 0
Embargo end date (OpenAIRE): 1970-01-01
Thesis comment: Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages: 27 str.
ID: 11880827