Asymptotic Behaviors Of Two Structured Population Models With Finite Delay

In this dissertation, within a semigroup framework and by using methods of Hille-Yosida operators, spectral analysis as well as the Perron-Frobenius theory, we investigate asymptotic behaviors of two structured population models with finite delay.This dissertation contains four chapters:In the first chapter, we briefly introduce some relevant background knowledge of structured population model. Then, in Chapter 2, by using semigroup, spectral analysis methods as well as the Perron-Frobenius theory, we discuss the locally asymptotic stability and asynchrony for a spatially and size-structured population model with delayed birth process. In Chapter 3, by similar methods and theo-ry, we discuss the locally asymptotic stability and asynchrony for an age-cycle structured cell model with delay. Finally, in Chapter 4, the results of this paper are given.Based on the existed work in literatures on the size/age-structured population models, we further consider in this dissertation the effects of delays in the birth process and spatial location on the asymptotic behaviours of the solutions. The methods and theory of delayed semigroup are applied here to discuss the problem. Our obtained conclusions extend and develop some corresponding existing results.