Asymptotic analysis of a spatially and size-structured population model with delayed birth process

This paper is devoted to the study of a spatially and size-structured population dynamics model with delayed birth process. Our focus is on the asymptotic behavior of the system, in particular on the effect of the spatial location and the time lag on the long-term dynamics. To this end, within a semigroup framework, we derive the locally asymptotic stability and asynchrony results respectively for the considered population system under some conditions. For our discussion, we use the approaches concerning operator matrices, Hille-Yosida operators, spectral analysis as well as Perron-Frobenius theory. We also do two numerical simulations to illustrate the obtained stability and asynchrony results.