Abstract: We consider a nonlinear age-structured population
dynamics model in which the population growth is dependent on a weighted
integral of the population density function There
exists an ideal weight function which
results in the “most stable” positive equilibrium. We prove that the
difference between the actual weight function w
and determines
the stability of the positive equilibrium. The stable region in the parameter
space w is an open absorbing set centered at the ideal weight function When
there
are oscillations of various extent, from damped to divergent and chaotic. We
show by numerical example that the extent of such oscillations is closely
related to the size of This
is a more precise stability result for single species age-structured population
model than existing ones and may focus experimental attention on the
significance and details of the weight function.
Keywords and phrases: population dynamics, age-structure, stability, oscillation.
