Application of stochastic differential equations and stochastic delay differential equations in population dynamics

Modelling population dynamics in random environment is a way of studying the fluctuations of population size that was affected by the stochasticity of the outside factors like weather. Marion et al. (2002) showed the ability of this environmental Brownian noise (if we assume weather effect follows B...

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Main Author:	Bahar, Arifah
Format:	Thesis
Language:	English
Published:	2005
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/4054/1/ArifahBaharPFS2005.pdf
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id	my-utm-ep.4054
record_format	uketd_dc
spelling	my-utm-ep.40542018-09-19T05:02:58Z Application of stochastic differential equations and stochastic delay differential equations in population dynamics 2005 Bahar, Arifah QA Mathematics Modelling population dynamics in random environment is a way of studying the fluctuations of population size that was affected by the stochasticity of the outside factors like weather. Marion et al. (2002) showed the ability of this environmental Brownian noise (if we assume weather effect follows Brownian noise) in suppressing population explosion, using model that is restricted by its hypothesis. Consequently, this restriction excludes model like power law logistic model. On the other hand, power logistic model has emerged as a good model for variety of natural phenomenas. Thus the exclusion of this model from Marion et al. (2002) model really define a gap in literature that need further work in order to adapt a new hypothesis. Thus this thesis expands their work in three different perspectives that is adapting new assumption to include power law logistic model, improving the existing estimate by means of addition and changing the way the noise is perturbed especially noise that is independent of population size, thus establishing a new way of proving nonnegative global solution and how to detect population extinction. Finally constant delay is also included into the model with some modification from the original model which the followed by the study of its nonnegative global solution, boundedness in s-th moment, asymptotic behaviour and also the intensed noise that may lead to population extinction. 2005 Thesis http://eprints.utm.my/id/eprint/4054/ http://eprints.utm.my/id/eprint/4054/1/ArifahBaharPFS2005.pdf application/pdf en public phd doctoral University of Strathclyde, Department of Statistics and Modelling Science Department of Statistics and Modelling Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Bahar, Arifah Application of stochastic differential equations and stochastic delay differential equations in population dynamics
description	Modelling population dynamics in random environment is a way of studying the fluctuations of population size that was affected by the stochasticity of the outside factors like weather. Marion et al. (2002) showed the ability of this environmental Brownian noise (if we assume weather effect follows Brownian noise) in suppressing population explosion, using model that is restricted by its hypothesis. Consequently, this restriction excludes model like power law logistic model. On the other hand, power logistic model has emerged as a good model for variety of natural phenomenas. Thus the exclusion of this model from Marion et al. (2002) model really define a gap in literature that need further work in order to adapt a new hypothesis. Thus this thesis expands their work in three different perspectives that is adapting new assumption to include power law logistic model, improving the existing estimate by means of addition and changing the way the noise is perturbed especially noise that is independent of population size, thus establishing a new way of proving nonnegative global solution and how to detect population extinction. Finally constant delay is also included into the model with some modification from the original model which the followed by the study of its nonnegative global solution, boundedness in s-th moment, asymptotic behaviour and also the intensed noise that may lead to population extinction.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Bahar, Arifah
author_facet	Bahar, Arifah
author_sort	Bahar, Arifah
title	Application of stochastic differential equations and stochastic delay differential equations in population dynamics
title_short	Application of stochastic differential equations and stochastic delay differential equations in population dynamics
title_full	Application of stochastic differential equations and stochastic delay differential equations in population dynamics
title_fullStr	Application of stochastic differential equations and stochastic delay differential equations in population dynamics
title_full_unstemmed	Application of stochastic differential equations and stochastic delay differential equations in population dynamics
title_sort	application of stochastic differential equations and stochastic delay differential equations in population dynamics
granting_institution	University of Strathclyde, Department of Statistics and Modelling Science
granting_department	Department of Statistics and Modelling Science
publishDate	2005
url	http://eprints.utm.my/id/eprint/4054/1/ArifahBaharPFS2005.pdf
_version_	1747814491002765312

Application of stochastic differential equations and stochastic delay differential equations in population dynamics

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