20.500.12556/RUL-176654 Analiza ljubezenskih dinamik s pomočjo matematičnih modelov magistrsko delo An analysis of romantic dynamics through mathematical modelling V magistrskem delu raziščemo kako lahko matematika prispeva k razumevanju iskanja pravega partnerja ter gradnji srečnega in stabilnega zakona. Ključno vprašanje je, zakaj se kljub želji in načrtovanju trajnega razmerja tolikšen delež zakonov konča z ločitvijo. Delo vsebuje pregled matematične literature, ki na različne načine razlaga in modelira ljubezenske odnose. Za analizo dinamike ljubezenskih razmerij glede na osebnostne značilnosti partnerjev so uporabljeni modeli dinamičnih sistemov. Začeli smo s preprostim linearnim modelom, nato pa postopoma vključili psihološke dejavnike, vpliv okolja ter dejavnike sodobne družbe. Tako dobimo vpogled v to ali je odnos stabilen ali nestabilen ter kako se razvija skozi čas. Kot ključen za dolgoročno srečen zakon se izkaže model, ki temelji na drugem zakonu termodinamike in teoriji optimalnega krmiljenja ter poudarja potrebo po stalnem vlaganju ravno prave količine truda v odnos. Ker pa na naše odločitve vplivajo tudi odločitve drugega partnerja, lahko razmerja zelo dobro razložimo s pomočjo teorije iger. Optimalna strategija za dolgoročno uspešen odnos je strategija zob za zob, ki jasno pokaže, kako se je smiselno odzivati na dejanja partnerja, če želimo graditi stabilen in zadovoljujoč odnos. S pomočjo zapornikove dileme in lova na jelena pokažemo, da sta za trajen odnos ključna zaupanje in sodelovanje. In this master’s thesis, we explore how mathematics can contribute to understanding the search for the right partner and the building of a happy and stable marriage. The key question is why, despite the desire and planning for a lasting relationship, such a large share of marriages ends in divorce. The thesis provides a review of mathematical literature that explains and models romantic relationships in various ways. To analyse the dynamics of relationships with respect to the partners’ personality traits, models of dynamical systems are used. We begin with a simple linear model and then gradually include psychological factors, environmental influences, and elements of modern society. This offers insight into whether a relationship is stable or unstable, as well as how it develops over time. A model based on the second law of thermodynamics and optimal control theory proves to be crucial for a long-term happy marriage, as it emphasises the need for continuous investment of just the right amount of effort in the relationship. Since our decisions are also influenced by those of the other partner, relationships can be convincingly explained through game theory. The optimal strategy for a long-term successful relationship is the tit-for-tat strategy, which clearly demonstrates how to respond to a partner’s actions in order to build a stable and fulfilling relationship. By applying the prisoner’s dilemma and the stag hunt, we show that trust and cooperation are essential for a lasting relationship. sistemi diferencialnih enačb stacionarne točke teorija iger lov na jelena zapornikova dilema strategija zob za zob teorija optimalnega krmiljenja drugi zakon termodinamike modeli odnosov problem tajnice ločitev srečen zakon systems of differential equations stationary points game theory stag hunt prisoner’s dilemma tit-for-tat strategy optimal control theory second law of thermodynamics relationship models secretary problem divorce happy marriage true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2025-12-07 08:15:06 2025-12-07 08:15:19 2025-12-23 04:02:34 0000-00-00 00:00:00 2025 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 156767 259984131 21034.pdf 21034.pdf 1 69D6763F4C0BA807058BBE55E252EFC3 406a0fdef3079204445268fd3cad3bf7f7fe43f1bc97195374aabb1764e6b37f 16464d9d-d33c-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=223126 Fakulteta za matematiko in fiziko 0 0 0