Stability analysis of two species mutualism mode with time delay and harvesting / Rusliza Ahmad

In this thesis, we analyze a two-species mutualism model with and without time delay and harvesting functions. The time delay is considered in the model to improve accuracy because the growth rate of the population depends not only on the present size of population but also on past information while...

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Main Author:	Ahmad, Rusliza
Format:	Thesis
Language:	English
Published:	2013
Online Access:	http://ir.uitm.edu.my/id/eprint/16438/ http://ir.uitm.edu.my/id/eprint/16438/1/TM_RUSLIZA%20AHMAD%20CS%2013_5.pdf

id	uitm-16438
recordtype	eprints
spelling	uitm-164382019-02-22T07:07:54Z http://ir.uitm.edu.my/id/eprint/16438/ Stability analysis of two species mutualism mode with time delay and harvesting / Rusliza Ahmad Ahmad, Rusliza In this thesis, we analyze a two-species mutualism model with and without time delay and harvesting functions. The time delay is considered in the model to improve accuracy because the growth rate of the population depends not only on the present size of population but also on past information while the harvesting function is introduced to describe the rate of removal of the species. The stability of the model involving time delay is determined by defining a time delay margin. The global stability analysis of the unique positive equilibrium point of mutualism model with two different harvesting functions is proven by constructing a suitable Lyapunov function. The two harvesting functions are harvesting at a constant rate and harvesting at a rate proportional to the population size. The effect of time delay and two different harvesting functions on the dynamics of the population has been examined. We consider time delay into the basic model without harvesting and discuss the effect of delay on the stability of the unique positive equilibrium point.From the analysis, it can be concluded that time delay can induce instability of a stable equilibrium point. The time delay model is then modified to include a harvesting function. Then we discuss the effect of harvesting and time delay on the dynamics of the model. The analysis shows that when there is no delay, varying the harvesting rate does not affect the stability of the model if the value of harvesting rate is under control while time delay can cause a stable equilibrium point to become unstable. 2013 Thesis NonPeerReviewed text en http://ir.uitm.edu.my/id/eprint/16438/1/TM_RUSLIZA%20AHMAD%20CS%2013_5.pdf Ahmad, Rusliza (2013) Stability analysis of two species mutualism mode with time delay and harvesting / Rusliza Ahmad. Masters thesis, Universiti Teknologi MARA.
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Teknologi MARA
building	UiTM Institutional Repository
collection	Online Access
language	English
description	In this thesis, we analyze a two-species mutualism model with and without time delay and harvesting functions. The time delay is considered in the model to improve accuracy because the growth rate of the population depends not only on the present size of population but also on past information while the harvesting function is introduced to describe the rate of removal of the species. The stability of the model involving time delay is determined by defining a time delay margin. The global stability analysis of the unique positive equilibrium point of mutualism model with two different harvesting functions is proven by constructing a suitable Lyapunov function. The two harvesting functions are harvesting at a constant rate and harvesting at a rate proportional to the population size. The effect of time delay and two different harvesting functions on the dynamics of the population has been examined. We consider time delay into the basic model without harvesting and discuss the effect of delay on the stability of the unique positive equilibrium point.From the analysis, it can be concluded that time delay can induce instability of a stable equilibrium point. The time delay model is then modified to include a harvesting function. Then we discuss the effect of harvesting and time delay on the dynamics of the model. The analysis shows that when there is no delay, varying the harvesting rate does not affect the stability of the model if the value of harvesting rate is under control while time delay can cause a stable equilibrium point to become unstable.
format	Thesis
author	Ahmad, Rusliza
spellingShingle	Ahmad, Rusliza Stability analysis of two species mutualism mode with time delay and harvesting / Rusliza Ahmad
author_facet	Ahmad, Rusliza
author_sort	Ahmad, Rusliza
title	Stability analysis of two species mutualism mode with time delay and harvesting / Rusliza Ahmad
title_short	Stability analysis of two species mutualism mode with time delay and harvesting / Rusliza Ahmad
title_full	Stability analysis of two species mutualism mode with time delay and harvesting / Rusliza Ahmad
title_fullStr	Stability analysis of two species mutualism mode with time delay and harvesting / Rusliza Ahmad
title_full_unstemmed	Stability analysis of two species mutualism mode with time delay and harvesting / Rusliza Ahmad
title_sort	stability analysis of two species mutualism mode with time delay and harvesting / rusliza ahmad
publishDate	2013
url	http://ir.uitm.edu.my/id/eprint/16438/ http://ir.uitm.edu.my/id/eprint/16438/1/TM_RUSLIZA%20AHMAD%20CS%2013_5.pdf
first_indexed	2023-09-18T22:56:04Z
last_indexed	2023-09-18T22:56:04Z
_version_	1777417862149832704

Stability analysis of two species mutualism mode with time delay and harvesting / Rusliza Ahmad

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