Matrix models of population theory.

dc.contributor.advisor	Banasiak, Jacek.
dc.contributor.author	Abdalla, Suliman Jamiel Mohamed.
dc.date.accessioned	2014-05-12T13:03:05Z
dc.date.available	2014-05-12T13:03:05Z
dc.date.created	2013
dc.date.issued	2013
dc.description	Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2013.	en
dc.description.abstract	Non-negative matrices arise naturally in population models. In this thesis, we first study Perron- Frobenius theory of non-negative irreducible matrices. We use this theory to investigate the asymptotic behaviour of discrete time linear autonomous models. Then we discuss an application for this in age structured population. Furthermore, we study Liapunov stability of a general non-linear autonomous model. We consider a general nonlinear autonomous model that arises in structured population. We assume that the associated nonlinear matrix of this model is non-increasing at all density levels. Then, we show the existence of global extinction. In addition, we show the stability condition of the extinction equilibrium of the this model in the Liapunov sense.	en
dc.identifier.uri	http://hdl.handle.net/10413/10697
dc.language.iso	en_ZA	en
dc.subject	Matrices.	en
dc.subject	Nonlinear difference equations.	en
dc.subject	Theses--Applied mathematics.	en
dc.title	Matrix models of population theory.	en
dc.type	Thesis	en

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