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The solution and the stability of a nonlinear age-structured population model

Published online by Cambridge University Press:  17 February 2009

Norhayati  and
G. C. Wake
Norhayati
Affiliation:
Department of Mathematics, University Brunei Darussalem, NegaraBrunei Darussalem; e-mail: yati@fos.ubd.edu.bn.
G. C. Wake
Affiliation:
Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand; e-mail: g.wake@math.canterbury.ac.nz.
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Abstract

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We consider an age-structured population model achieved by modifying the classical Sharpe-Lotka-McKendrick model, incorporating an overcrowding effect or competition for resources term. This term depends on the whole population rather than on any specific age group, in the case of overcrowding or limitation of resources. We investigate the solutions for arbitrary initial conditions. We consider the existence of a steady age distribution and its stability and are able to determine this for a simple illustrative case. If the non-trivial steady age distribution is unstable, there is a critical initial population size beyond which the population explodes. This watershed is independent of the shape of the initial age distribution.

Type
Research Article
Information
The ANZIAM Journal , Volume 45 , Issue 2 , October 2003 , pp. 153 - 165
Copyright
Copyright © Australian Mathematical Society 2003

References

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