The Numerical Bifurcation Analysis Of Leslie-Gower Predator-Prey Model With Different Types Of Predator Harvesting Strategies

The predator-prey model is the most common model dealing with the interaction between two species. The dynamics of a predator-prey model has attracted a lot of attention from many ecologists and mathematicians. This study shows theoretical and numerical results on the analysis of the Leslie-Gower pr...

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Main Author: Ahmad, Fazilah
Format: Thesis
Language:English
Published: 2023
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Online Access:http://eprints.usm.my/60279/1/24%20Pages%20from%20FAZILAH%20BINTI%20AHMAD.pdf
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spelling my-usm-ep.602792024-03-26T01:09:51Z The Numerical Bifurcation Analysis Of Leslie-Gower Predator-Prey Model With Different Types Of Predator Harvesting Strategies 2023-05 Ahmad, Fazilah QA1 Mathematics (General) The predator-prey model is the most common model dealing with the interaction between two species. The dynamics of a predator-prey model has attracted a lot of attention from many ecologists and mathematicians. This study shows theoretical and numerical results on the analysis of the Leslie-Gower predator-prey model with different types of predator harvesting strategies namely linear, constant-yield and nonlinear predator harvesting models. We illustrate the numerical bifurcations analysis of codimension-one and codimension-two to show the stability of the steady-states and the behaviour of the model when the harvesting rate change under different harvesting strategies. We analyse each model to determine the existence of local bifurcations such as saddle-node, transcritical, Hopf, and Bogdanov-Takens bifurcations and compare the different type of bifurcations that occurs for each predator harvesting strategy. This study investigates the dynamics of the Leslie-Gower predator-prey model with different harvesting strategies through numerical analysis that corroborate with the critical harvesting rate determined from the theoretical analysis. This study also discovers the significance of predator harvesting strategies in the optimal management of renewable resources using the Leslie-Gower predator-prey model. The choice of the parameter values is crucial with the small difference in the values may cause the predator species extinct if the harvesting rate is greater than the critical harvesting rate. 2023-05 Thesis http://eprints.usm.my/60279/ http://eprints.usm.my/60279/1/24%20Pages%20from%20FAZILAH%20BINTI%20AHMAD.pdf application/pdf en public masters Perpustakaan Hamzah Sendut Pusat Pengajian Sains Matematik
institution Universiti Sains Malaysia
collection USM Institutional Repository
language English
topic QA1 Mathematics (General)
spellingShingle QA1 Mathematics (General)
Ahmad, Fazilah
The Numerical Bifurcation Analysis Of Leslie-Gower Predator-Prey Model With Different Types Of Predator Harvesting Strategies
description The predator-prey model is the most common model dealing with the interaction between two species. The dynamics of a predator-prey model has attracted a lot of attention from many ecologists and mathematicians. This study shows theoretical and numerical results on the analysis of the Leslie-Gower predator-prey model with different types of predator harvesting strategies namely linear, constant-yield and nonlinear predator harvesting models. We illustrate the numerical bifurcations analysis of codimension-one and codimension-two to show the stability of the steady-states and the behaviour of the model when the harvesting rate change under different harvesting strategies. We analyse each model to determine the existence of local bifurcations such as saddle-node, transcritical, Hopf, and Bogdanov-Takens bifurcations and compare the different type of bifurcations that occurs for each predator harvesting strategy. This study investigates the dynamics of the Leslie-Gower predator-prey model with different harvesting strategies through numerical analysis that corroborate with the critical harvesting rate determined from the theoretical analysis. This study also discovers the significance of predator harvesting strategies in the optimal management of renewable resources using the Leslie-Gower predator-prey model. The choice of the parameter values is crucial with the small difference in the values may cause the predator species extinct if the harvesting rate is greater than the critical harvesting rate.
format Thesis
qualification_level Master's degree
author Ahmad, Fazilah
author_facet Ahmad, Fazilah
author_sort Ahmad, Fazilah
title The Numerical Bifurcation Analysis Of Leslie-Gower Predator-Prey Model With Different Types Of Predator Harvesting Strategies
title_short The Numerical Bifurcation Analysis Of Leslie-Gower Predator-Prey Model With Different Types Of Predator Harvesting Strategies
title_full The Numerical Bifurcation Analysis Of Leslie-Gower Predator-Prey Model With Different Types Of Predator Harvesting Strategies
title_fullStr The Numerical Bifurcation Analysis Of Leslie-Gower Predator-Prey Model With Different Types Of Predator Harvesting Strategies
title_full_unstemmed The Numerical Bifurcation Analysis Of Leslie-Gower Predator-Prey Model With Different Types Of Predator Harvesting Strategies
title_sort numerical bifurcation analysis of leslie-gower predator-prey model with different types of predator harvesting strategies
granting_institution Perpustakaan Hamzah Sendut
granting_department Pusat Pengajian Sains Matematik
publishDate 2023
url http://eprints.usm.my/60279/1/24%20Pages%20from%20FAZILAH%20BINTI%20AHMAD.pdf
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