Stability Analysis For A Size-Structured Cannibalism Population Model

In this dissertation, we mainly carry out the stability and asynchrony analysis for a size-structured cannibalism model with delayed birth process. We first transfer the considered model into a Cauchy problem of abstract evolution equations, and we prove the existence and uniqueness of solutions by using the theory of strongly continuous semigroup. Then, through the analysis of resolvent operators and compact semigroup, we investigate the regularity for the generated semigroup, and obtain the characteristic equa-tions. We establish successfully the conditions of stability and asynchrony for stationary solutions of the population system.Based on the existing work in literatures on the size-structured cannibalism popula-tion models, we further consider in this dissertation the effects of delay in the birth process on the asymptotic behaviors of the population system. The theory and the techniques of delayed semigroup are applied here to discuss the problems. Our obtained results develop and extend the corresponding existing conclusions.