ANZIAM J.
45 (2003), 153-165
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The solution and the stability of a nonlinear age-structured population model
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Norhayati
Department of Mathematics
University Brunei Darussalem
Negara Brunei Darussalem
yati@fos.ubd.edu.bn
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G. C. Wake
Department of Mathematics and Statistics
University of Canterbury
Private Bag 4800
Christchurch
New Zealand
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.
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