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Systems of differential equations and interactions between two populations

Sabina Šubic (2017) Systems of differential equations and interactions between two populations. MSc thesis.

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    Abstract

    In this thesis we deal with mathematical models that illustrate the growth of two populations, which influence each other and between them appears one of the three main potential interactions between two populations: competition for resources, predation or symbiosis. We begin by examining the two-dimensional linear systems of differential equations – more precisely examining the way of finding solutions of two-dimensional linear homogeneous systems of two differential equations. Then we dedicate to two-dimensional nonlinear autonomous system and its linearization around fixed points. This allows us to study three mathematical models of different interactions between two populations, which also conclude the study.

    Item Type: Thesis (MSc thesis)
    Keywords: systems of differential equations, autonomous systems, phase plane, linearization, population dynamics
    Number of Pages: 74
    Language of Content: Slovenian
    Mentor / Comentors:
    Mentor / ComentorsIDFunction
    izr. prof. dr. Marko SlaparMentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=50126&select=(ID=11704137)
    Institution: University of Ljubljana
    Department: Faculty of Education
    Item ID: 4674
    Date Deposited: 14 Sep 2017 09:30
    Last Modified: 14 Sep 2017 09:30
    URI: http://pefprints.pef.uni-lj.si/id/eprint/4674

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