20.500.12556/RUL-122255 Poincaré-Bendixsonov izrek delo diplomskega seminarja Poincaré-Bendixson theorem 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. 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. dinamični sistemi limitna množica modeliranje fazni portret Poincaré-Bendixsonov izrek sistemi nelinearnih diferencialnih enačb tokovnice dynamical systems limit cycle modelling phase portrait Poincaré-Bendixson theorem systems of nonlinear differential equations trajectories true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2020-12-02 08:15:02 2020-12-02 08:15:06 2024-05-29 14:26:29 0000-00-00 00:00:00 2020 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.93 116389 58375939 1543.pdf 1543.pdf 1 71D09AACCAFCFC90EE37623E913D1978 6361363ad9328496bb61d9af46ffad7d94c60a248f05ae0d7517f23ece962564 14f5e4d3-a1bb-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=137440 Fakulteta za matematiko in fiziko 0 0 0