On The Analysis And Control For Discrete Age-Structured Population Models

Modeling and analysis of biological populations have been palying an important role in the study of population evolution and the relationship between species and their habitats. There is a long history for research on the discrete age-structured population models, and lots of results are estalished. Biologists and mathematicians had made use of linear models in early studies, and the relevant research results have been relatively perfect. The study of nonlinear population models with age-structure began in early 1970s, and much progress was made. Since that P. H. Leslie proposed the first discrete population model in 1945, many scholars began to study population dynamics from the angle of discretization. A seemingly simple mathematical model may has a complex dynamic behavior, such as chaos. For discrete populations model with age-structure, one can not only consider the survival and development trend of the populations, but also discuss the harvest (fishing, cutting etc) problem, which has positive significance for the use and management of renewable resource.In this dissertation, several kinds of population dynamic models with age-structure are analyzed, the focus is on the existence of equilibria and their stability. By the use of matrix theory, dynamic program, bifurcation theory and fuzzy mathematics, some new results are obtained, which provide a helpful reference for the practical applications.The research results are included in two parts: chapters 2 and 3.In chapter 2, one kind of discrete age-stuctured population model is analyzed, and the existence , stability of equilibria, conditions for stability are discussed by matrix and bifurcation theory. In adition, we have considered multispecies situation, and the survival trend, the formula of net reproductive number, the conditions for equilibria stablity are obtained. Finally, Matlab and Maple are used for numerical simulations and explanation of the effectiveness and feasibility.In chapter 3, the harvest problem of discrete age-structured population model is discussed. By means of the fuzzy mathematics and dynamic program, the optimal harvest strategy is got. Again we use Matlab and Maple to test the conclusion of this chapter.