ANZIAM  J.  45 (2003), 153-165
The solution and the stability of a nonlinear age-structured population model

  Department of Mathematics
  University Brunei Darussalem
  Negara Brunei Darussalem
G. C. Wake
  Department of Mathematics and Statistics
  University of Canterbury
  Private Bag 4800
  New Zealand

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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