Asymptotic behaviors of a size-structured population model

In this paper we devote ourselves to the study of the asymptotic behavior of a size-structured population dynamics with random diffusion and delayed birth process. Within a semigroup framework, we discuss the local stability and asynchrony respectively for the considered population system under some conditions. We use for our discussion the techniques of operator matrices, Hille-Yosida operators, positivity, spectral analysis as well as Perron-Frobenius theory.