delo diplomskega seminarja
Karmen Zupančič (Author), Uroš Kuzman (Mentor)

Abstract

V diplomski nalogi obravnavam avtonomne dinamične sisteme, ki so v ravnini podani s sistemom dveh diferencialnih enačb. Osrednji cilj diplome je dokaz in uporaba Poincaré-Bendixsonovega izreka. Omenjeni izrek opredeljuje možna limitna vedenja omejenih tokovnic, zato je zelo uporaben pri napovedovanju obnašanja tovrstnih sistemov pri velikih časih. V tem delu bomo izrek aplicirali na ekonomskem modelu, ki vključuje strukturne spremembe. Do slednjih v ekonomiji pride zaradi različnih dejavnikov, kot so na primer spremembe v razvoju gospodarstva ali pomanjkanje sredstev. V nalogi bomo pokazali, kako lahko vse te dejavnike ponazorimo z dinamičnim sistemom, katerega obnašanje je po Poincaré-Bendixsonovem izreku predvidljivo. Natančneje, izpeljali in obravnavali bomo Kaldorjev model, ter ga razširili na področje slovenskega zdravstva.

Keywords

dinamični sistemi;limitna množica;modeliranje;fazni portret;Poincaré-Bendixsonov izrek;sistemi nelinearnih diferencialnih enačb;tokovnice;

Data

Language: Slovenian
Year of publishing:
Typology: 2.11 - Undergraduate Thesis
Organization: UL FMF - Faculty of Mathematics and Physics
Publisher: [K. Zupančič]
UDC: 517.93
COBISS: 58375939 Link will open in a new window
Views: 916
Downloads: 143
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Other data

Secondary language: English
Secondary title: Poincaré-Bendixson theorem
Secondary abstract: In my diploma thesis I deal with autonomous dynamical systems in a plane given by a system of two differential equations. The central goal of the diploma is the proof and application of the Poincare-Bendixson theorem. The mentioned theorem defines the possible limit behaviors of bounded trajectories, so it is very useful in predicting the behavior of these systems at large times. In the paper, we will apply the theorem to the economic model, which includes structural changes. These occur due to various factors in the economy, such as changes in economic development or lack of resources. We will show how all of these factors can be illustrated by a dynamic system whose behavior is predictable according to Poincare-Bendixson's theorem. More precisely, we will implement and discuss the Kaldor model, and expand it to the field of Slovenian healthcare.
Secondary keywords: dynamical systems;limit cycle;modelling;phase portrait;Poincaré-Bendixson theorem;systems of nonlinear differential equations;trajectories;
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, Finančna matematika - 1. stopnja
Pages: 26 str.
ID: 12212340