Metuljev učinek : delo diplomskega seminarja

Meglić, Tadej (author), Prezelj, Jasna (mentor)

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.

• Language: Slovenian
• Keywords: kaos, dinamični sistem, diferencialne enačbe, bifurkacija
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2020
• PID: 20.500.12556/RUL-117237
• UDC: 517.9
• COBISS.SI-ID: 58558979
• Publication date in RUL: 03.07.2020

MEGLIĆ, Tadej, 2020, Metuljev učinek : delo diplomskega seminarja [online]. Bachelor’s thesis. [Accessed 26 April 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=117237

Secondary language

• Language: English
• Title: Butterfly effect

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.

• Keywords: chaos, dynamical system, differential equations, bifurcation