Stabilnost sustava diferencijskih jednadžbi

master's thesis

• Author: Antonija Jurković
• Mentor: Maja Starčević (mentor)
• Committee member: Zvonimir Tutek (predsjednik povjerenstva)
• Committee member: Marko Tadić (član povjerenstva)
• Committee member: Bojan Basrak (član povjerenstva)
• Committee member: Maja Starčević (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-07-10, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovome se radu primarno proučava kvalitativna teorija sustava diferencijskih jednadžbi s posebnim naglaskom na stabilnost točaka ravnoteže. Sustavi diferencijskih jednadžbi su iznimno važni jer opisuju mnoge procese u prirodi te promjene i odnose u znanostima poput ekonomije, strojarstva, građevine te općenito u tehničkim znanostima. U radu je posebna pozornost posvećena stabilnosti točaka ravnoteže sustava jednadžbi te smo detaljno obradili različite kriterije stabilnosti. U prvom smo poglavlju dali osnovne teoreme stabilnosti te smo riješili nekoliko primjera diferencijskih jednadžbi. Drugo poglavlje daje osnovnu teoriju sustava diferencijskih jednadžbi. U trećem poglavlju smo analizirali faznu ravninu, definirali Ljapunovljevu funkciju te primijenili Ljapunovljev teorem.

Abstract (english)

In this graduate work we studied qualitative theory of systems of difference equations with special accent on equilibrium points. Systems of difference equations are extremely important because they describe numerous models in natural sciences, economy, engineering, etc. In this work we especially observed stability of equilibrium points of systems of equations. We also thoroughly observed different criteria of stability. In the first chapter we gave some basic stability theorems and we solved several examples of difference equations. The second chapter gives basic theory of systems of difference equations. In the third chapter we did the phase space analysis and we also defined Liapunov functions and applied the Liapunov theorem.

• Keywords: sustav diferencijskih jednadžbi; stabilnost točaka ravnoteže; Ljapunovljeve funkcije; Ljapunovljev teorem
• Keywords (english): system of difference equations; equilibrium points; Liapunov functions; Liapunov theorem
• Language: croatian
• URN:NBN: urn:nbn:hr:217:169590
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Access restricted to students and staff of home institution
• Created on: 2019-02-04 10:07:29