Stability Of Biological Systems And Biological Resources, Optimal Development,

This paper discuss mainly globally asymptotically stability of uniform steady-state of biological system which is governed by partial differential equations, and the existence of periodic solution for impulsive equations or difference equations, meanwhile, the optimal harvest policy with impulsive harvest is considered. This paper include most of research work when the author persue her Ph.D. degree.The whole contents is divided into five chapters.Chapter 1, as the beginning of this paper, is given by some relative knowledge, such as preliminary theory of reaction-diffusion equations, calculus rule, and basis of partial functional differential equations.Chapter 2 and 3, as the second part of this thesis, focuses on the optimal exploitation of biological resource. As we all know, the optimal exploitation and utilization of biologic resources, has much significance to study, and many authors have studied this problem, but they often consider only continuous harvest or exploitation for some resource, and suppose distribution of the population is homogeneous, namely, they only are functions of time and are independent of spatial location. This is an ideal model. Based on this reason, Chapter 2 mainly deals with single species of nonhomogeneous spatial distribution with different harvest functions, and gain the corresponding optimal harvest policy. Chapter 3, combined the feasible principle, specially consider supposition of impulsive harvest and study sustainable development of biologic resources under the impulsive harvest, derive the existence and global asymptotically stability of impulsive periodic solution, furthermore, the optimal harvest policy is obtained.Chapter 4, consists of three different reaction-diffusion predator-prey models of partial differential equations with age-structured, in-cluding under the harvesting condition and in a polluted enviornment, and cross-diffusion besides self-diffusion , study the global asymptotical stability of uniform steady state, we compare the role of diffusion for stability.Chapter 5, using the coincidence degree and the priori estimations, discuss the nonautonomous difference equations and impulsive differential equations, including a food-chain system and a cooperative systems.At the end of the paper, it is proposed the remark of this paper and the further study direction, many related references are listed.