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In this paper, the global attractivity of the homogeneous equilibrium solution for the diffusive age-structured model $$ textstylebegin{cases} frac{partial u}{partial t}+frac{partial u}{partial a}=D(a)frac{ partial^{2}{u}}{partial x^{2}}-d(a)u, u0026 tgeq t_{0}geq A_{l}u003e0, a geq 0, 0 0, 0 0, 0 0, a geq 0, end{cases} $$is established when the diffusion and death rates, (D(a)) and (d(a)), respectively, are age dependent during the whole life of the species, and when the birth function (f(w)) is nonmonotone. In the paper, we also present some demonstrative examples.

Global attractivity in a non-monotone age-structured model with age-dependent diffusion and death rates