Abstract
We study the large time behaviour of a nonlinear population model with a general logistic term. It is proved that every solution must have a limit when time becomes infinite. We present conditions that guarantee the boundedness of the solution. Furthermore, we prove that in general no oscillation is possible for the total number of population. This is in sharp contrast to the linear case.
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This work was carried out with the aid of a grant from the International Development Centre, Ottawa, Canada
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Chan, W.L., Guo, B.Z. Global behaviour of age-dependent logistic population models. J. Math. Biol. 28, 225–235 (1990). https://doi.org/10.1007/BF00163146
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DOI: https://doi.org/10.1007/BF00163146