Neke primjene linearne algebre

master's thesis

• Author: Igor Kosturin
• Mentor: Ljiljana Arambašić (mentor)
• Committee member: Ljiljana Arambašić (predsjednik povjerenstva)
• Committee member: Marko Tadić (član povjerenstva)
• Committee member: Boris Širola (član povjerenstva)
• Committee member: Tina Bosner (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 ovom radu proučavamo tri matematička modela za neke pojednostavljene probleme populacijske dinamike. U prvom poglavlju analiziramo Leslijev model rasta populacije te matricu koja ga definira. Određivanjem svojstvenih vrijednosti Leslijeve matrice, opisujemo način pomoću kojeg možemo odrediti strukturu populacije nakon duljeg vremenskog perioda. Drugo poglavlje opisuje pojednostavljeni model za sječu šume čija su stabla podijeljena u visinske razrede. Model će zadovoljavati uvjete održivosti sječe i maksimiziranog prihoda od pojedine sječe. Treće poglavlje se bavi problemom maksimiziranja prihoda od izlova jedinki neke životinjske populacije pri čemu taj izlov mora biti kontroliran, a distribucija jedinki po dobnim razredima prije i poslije izlova jednaka.

Abstract (english)

In this thesis, we examine three simplified mathematical models of population dynamics. First chapter analyzes the Leslie model of population growth and matrix that defines it. By determining the eigenvalues of the Leslie matrix, we describe a method which can give us the structure of population after longer time period. Second chapter describes a simplified model for a forest harvesting whose trees are classified by height. The model requires that the harvest is sustainable and the yield obtained of each harvest is maximum. Third chapter deals with a problem of maximizing of a yield that is obtained by a sustainable animal population harvesting. Distribution of animal population has to be the same before and after harvesting.

• Keywords: problemi populacijske dinamike; Leslijev model rasta populacije; Leslijeva matrica
• Keywords (english): population dynamics; Leslie model of population growth; Leslie matrix
• Language: croatian
• URN:NBN: urn:nbn:hr:217:724007
• 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: 2019-02-15 12:15:59