Stability analysis of two species mutualism model 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
Subjects:	QA Mathematics Data processing
Online Access:	https://ir.uitm.edu.my/id/eprint/16438/2/16438.pdf
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spelling	my-uitm-ir.164382024-05-30T02:46:13Z Stability analysis of two species mutualism model with time delay and harvesting / Rusliza Ahmad 2013-12 Ahmad, Rusliza QA Mathematics Mathematical statistics. Probabilities Data processing 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. 2013-12 Thesis https://ir.uitm.edu.my/id/eprint/16438/ https://ir.uitm.edu.my/id/eprint/16438/2/16438.pdf text en public mphil masters Universiti Teknologi MARA Faculty of Computer and Mathematical Sciences Budin, Harun (Associate Professor Dr) Ismail, Salemah (Associate Professor Dr)
institution	Universiti Teknologi MARA
collection	UiTM Institutional Repository
language	English
advisor	Budin, Harun (Associate Professor Dr) Ismail, Salemah (Associate Professor Dr)
topic	QA Mathematics QA Mathematics Data processing
spellingShingle	QA Mathematics QA Mathematics Data processing Ahmad, Rusliza Stability analysis of two species mutualism model with time delay and harvesting / Rusliza Ahmad
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
qualification_name	Master of Philosophy (M.Phil.)
qualification_level	Master's degree
author	Ahmad, Rusliza
author_facet	Ahmad, Rusliza
author_sort	Ahmad, Rusliza
title	Stability analysis of two species mutualism model with time delay and harvesting / Rusliza Ahmad
title_short	Stability analysis of two species mutualism model with time delay and harvesting / Rusliza Ahmad
title_full	Stability analysis of two species mutualism model with time delay and harvesting / Rusliza Ahmad
title_fullStr	Stability analysis of two species mutualism model with time delay and harvesting / Rusliza Ahmad
title_full_unstemmed	Stability analysis of two species mutualism model with time delay and harvesting / Rusliza Ahmad
title_sort	stability analysis of two species mutualism model with time delay and harvesting / rusliza ahmad
granting_institution	Universiti Teknologi MARA
granting_department	Faculty of Computer and Mathematical Sciences
publishDate	2013
url	https://ir.uitm.edu.my/id/eprint/16438/2/16438.pdf
_version_	1804889565630038016

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

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