A. Calsina et J. Saldana, ASYMPTOTIC-BEHAVIOR OF A MODEL OF HIERARCHICALLY STRUCTURED POPULATION-DYNAMICS, Journal of mathematical biology, 35(8), 1997, pp. 967-987
A hierarchically structured population model with a dependence of the
vital rates on a function of the population density (environment) is c
onsidered. The existence, uniqueness and the asymptotic behaviour of t
he solutions is obtained transforming the original non-local PDE of th
e model into a local one. Under natural conditions, the global asympto
tical stability of a nontrivial equilibrium is proved. Finally, if the
environment is a function of the biomass distribution, the existence
of a positive total biomass equilibrium without a nontrivial populatio
n equilibrium is shown.