Predator-prey model with constant rate of harvesting

Predator-prey model is the first model to illustrate the interaction between predators and prey. It is a topic of great interest for many ecologists and mathematicians. This model assumes that the predator populations have negative effects on the prey populations. The generalized equation of this mo...

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محفوظ في:
التفاصيل البيبلوغرافية
المؤلف الرئيسي: Arifin, Nurul Aina
التنسيق: أطروحة
اللغة:English
منشور في: 2014
الموضوعات:
الوصول للمادة أونلاين:http://eprints.utm.my/id/eprint/48587/1/NurulAinaArifinMFS2014.pdf
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spelling my-utm-ep.485872020-02-05T08:58:27Z Predator-prey model with constant rate of harvesting 2014 Arifin, Nurul Aina QA Mathematics Predator-prey model is the first model to illustrate the interaction between predators and prey. It is a topic of great interest for many ecologists and mathematicians. This model assumes that the predator populations have negative effects on the prey populations. The generalized equation of this model is the response of the populations would be proportional to the product of their population densities. Prey population grows with limited by carrying capacity, K and it is called the logistic equation. Thus, in this research, there are four different cases are analyzed which are predator-prey model, predator-prey model with harvesting in prey, predator-prey model with harvesting in predator and predator-prey model with harvesting in both populations. Systems of ordinary differential equation are used for all models. The objectives of this research are i) to study the concept of Lotka-Volterra predator-prey model, ii) to analyze the predator-prey model with constant rate of harvesting in prey, iii) to analyze the predator-prey model with constant rate of harvesting in predator, iv) to analyze the predator-prey model with constant rate of harvesting in both populations. In analyzing all four models, equilibrium points will be obtained and analyzed for the stability by using Routh-Hurwitz Criteria. Lastly, some numerical examples and graphical analysis are shown to illustrate the stability of the stable equilibrium points and the effects of harvesting to the systems. 2014 Thesis http://eprints.utm.my/id/eprint/48587/ http://eprints.utm.my/id/eprint/48587/1/NurulAinaArifinMFS2014.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:79469?queryType=vitalDismax&query=Predator-prey+model+with+constant+rate+of+harvesting&public=true masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution Universiti Teknologi Malaysia
collection UTM Institutional Repository
language English
topic QA Mathematics
spellingShingle QA Mathematics
Arifin, Nurul Aina
Predator-prey model with constant rate of harvesting
description Predator-prey model is the first model to illustrate the interaction between predators and prey. It is a topic of great interest for many ecologists and mathematicians. This model assumes that the predator populations have negative effects on the prey populations. The generalized equation of this model is the response of the populations would be proportional to the product of their population densities. Prey population grows with limited by carrying capacity, K and it is called the logistic equation. Thus, in this research, there are four different cases are analyzed which are predator-prey model, predator-prey model with harvesting in prey, predator-prey model with harvesting in predator and predator-prey model with harvesting in both populations. Systems of ordinary differential equation are used for all models. The objectives of this research are i) to study the concept of Lotka-Volterra predator-prey model, ii) to analyze the predator-prey model with constant rate of harvesting in prey, iii) to analyze the predator-prey model with constant rate of harvesting in predator, iv) to analyze the predator-prey model with constant rate of harvesting in both populations. In analyzing all four models, equilibrium points will be obtained and analyzed for the stability by using Routh-Hurwitz Criteria. Lastly, some numerical examples and graphical analysis are shown to illustrate the stability of the stable equilibrium points and the effects of harvesting to the systems.
format Thesis
qualification_level Master's degree
author Arifin, Nurul Aina
author_facet Arifin, Nurul Aina
author_sort Arifin, Nurul Aina
title Predator-prey model with constant rate of harvesting
title_short Predator-prey model with constant rate of harvesting
title_full Predator-prey model with constant rate of harvesting
title_fullStr Predator-prey model with constant rate of harvesting
title_full_unstemmed Predator-prey model with constant rate of harvesting
title_sort predator-prey model with constant rate of harvesting
granting_institution Universiti Teknologi Malaysia, Faculty of Science
granting_department Faculty of Science
publishDate 2014
url http://eprints.utm.my/id/eprint/48587/1/NurulAinaArifinMFS2014.pdf
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