The Optimal Harvest Policy Of Two Species Model With Several Types Of Stage Structures

The survival and development of biological population all cannot do without its living environment, in the resource limited environment, natural law of the jungle wild animal can long survive? With the increasing environmental pollution and overfishing, mysterious and vast marine organisms will be reduced, or even extinction? In the control of pests, replaced by releasing natural enemy to spray pesticides over, the benign development of ecological system? In order to ensure the biodiversity of nature, plays an important role in the persistence of species.Differences in biological model establishment often overlook the ability to survive in the population with different growth process, often assume that populations in the birth, growth and survival ability is immutable and frozen in the process of ripening and senescence. But the fact is not so, for many populations in nature, its birth, there is a close relationship between predation and survival ability and the environment. With the physiological characteristics of the population at some stage during the whole life (such as birth, feeding and survival ability and so on) one of the most common phenomenon in nature. In all stages of its growth will show different characteristics, which affect the permanence and extinction of species. The species is divided into different stage model to study, get the attention and research of many scholars at home and abroadIn this paper, on the basis of previous research results, based on the single population model with stage structure of Chen Lansun structure, establish some kinds of model of two species with stage, including; acquisition strategy of a kind of competition model with stage structure predator-prey model, two species are the best mutual model with stage structure and capture strategy and two species with stage structure while capturing the optimal harvesting policy. These types of model are discussed more practical results.This paper mainly uses the stability theory of ordinary differential equation and optimal control theory to obtain the persistence model, local and global stability of positive equilibrium conditions, and derive the optimal harvesting policy, provide some guidance for the persistence of biological population.Mainly from the following three aspects(Ⅰ) Acquisition strategy of a kind of competition model with stage structure is optimalIn the second chapter, firstly the image system simplification using specific curve obtained for the existence and uniqueness of the positive equilibrium conditions, the Routh-Hurwith the-orem for the local system at the positive equilibrium point asymptotically stable conditions, and then construct a suitable Liapunov function to find the global stability of the positive equilib-rium conditions in the system, the use of Pontryagin maximum principle necessary conditions and the maximum value of the derived the optimal harvesting policy.(Ⅱ) The optimal harvesting policy capture reciprocal model with stage structure of two species were simultaneously.In the third chapter, the two populations were studied with stage structure and optimal control problems at the same time, acquisition, use of biological characteristics will simplify the existence and uniqueness of positive equilibrium conditions, the Routh-Hurwith theorem for the local system at the positive equilibrium is asymptotically stable condition, and then construct a suitable Liapunov function the global stability of the positive equilibrium conditions in the system, at last by using Pontryagin maximum principle necessary conditions and the maximum value of the derived the optimal harvesting policy.(Ⅲ) Two species predator-prey model with stage structure and capture the optimal har-vesting policy. In the fourth chapter, the two populations were studied with stage structure and optimal prey predator model also captures the control problem, which assumes only adult predator prey predator of adult, juvenile predators prey so as to reduce the mortality of juvenile. Use the same method to discuss the unique positive equilibrium point, local asymptotic stability and global asymptotic stability conditions and derived the optimal harvesting policy.