Sistemi diferencialnih enačb in interakcije med dvema populacijama
V magistrskem delu obravnavamo matematične modele, ki ponazarjajo rast dveh populacij, ki vplivata druga na drugo, in sicer se med njima pojavlja ena od treh osnovnih možnih interakcij med dvema populacijama: tekmovanje za vire, plenjenje ali simbioza. Začenjamo s proučevanjem dvodimenzionalnih linearnih sistemov diferencialnih enačb – natančneje z načinom iskanja rešitev homogenih dvodimenzionalnih linearnih sistemov dveh diferencialnih enačb. V nadaljevanju se nato posvetimo dvodimenzionalnim nelinearnim avtonomnim sistemom ter njihovi linearizaciji okrog stacionarnih točk. Vse to nam v glavnem delu omogoča obravnavo matematičnih modelov treh interakcij med dvema populacijama, s čimer tudi zaključimo magistrsko delo.
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.
2017
2017-09-16 03:00:47
1060
avtonomni sistemi, fazna ravnina, linearizacija, populacijska dinamika,
mathematics, matematika,
mb22
[S. Šubic]
Sabina
Šubic
70
Marko
Slapar
991
UDK
4
51(043.2)
COBISS_ID
3
11704137
0
Predstavitvena datoteka
2017-09-16 03:00:48