| The ecological environment was composed of the colorful and diversity boilog-ical species, because of this, Darwin pointed, Evolutionary Biology was called fight-ing for living. One species need other species for food to living, being based on this, Allee effect exists in general species. Everyone has their special charactics, they change from time to time, the genetic code, the age and the life’s upon and down, all of this, which determined their action on a certain time. In other words, there are no two identical leaves in the world, the same applies to species. Each species has being changing themselves. Different species are interdependent and interactional to form a stable biosphere. For this reason, it ensured the diversity of biological species, further to say, it relieve stress for other species and resources, especially for people to live longly. Theories and experiments show that Allee effect is widespread and it has a profound impact on the ecological balance and protection of biological diversity. The existence and the deterioration of resources issue also let human make the sustainable use of the resource. So the de-mand of biological resources should be rational and sensible, only in this way, it can give full play to the renewable advantage of biological resources. In recent years, these is a lot of literatures on the study of the Allee effect and harvest rate, at the same time, it is limited for combining two of them. In view of this, this manuscript from the point of two views, the research has discussed predator-prey system with the Allee effect; Stability analysis of mutualistic-parasitic coupled system with harvesting rate for parasitifer groups.Then we get the following conclusions:The co-veolution between parasite and its host is one of the most important research field in both population ecology and biological forecasting, such as crop cultivation, live stock breeding, excessive copies of pathogenic cell, and so on. Be based on the assumption that parasites might facilitate the host population increase. We talked about the stability analysis of mutualistic-parasitic coupled system with harvesting rate for parasitifer groups., Firstly, we introduce the inherent promotion level K into an intergration model of Lotka-Volterra and Leslie type, then established a mutualistic-parasitic coupled system. Using different equation stability theory, we find that the behavior dynamics of the system closely associate with the inherent promotion level parameter K.With the increasing of the human social activities, at the same time, as a result of the industrialization, globalization and the integration, the ecological environment was badly destroyed and it has an unfriendly influence on organisms to live. For small populations, it is more easily affected than others. In addition, we having discussing The study for predator-prey system with Allee effect exist in prey population and apositical reaction exist in predator meanwhile discussed the existence of the equilibrium and global stability of the positive equilibrium, we use Matlab to simulate and get the more general conclusions. This chapter studied I type function system model,we have imitated the system through the Matlab and got the evolution phase of prey and predator with Allee effect and the evolution phase of prey and predator without Allee effect. As the result showed, the evolution of the system belong to an ideal situation without Allee effect which is bab for living beings’evolution. Whereas, the evolution of the system with Allee effect spend more time than the evolution of the system without Allee effect, so it is much more reasonable to take the system with Allee effect into consideration. Allee effect supported the most important theoretical foundation for the management of endangered species and it has a guiding effect to the administrative department.Finally, a predator-prey system with Allee effect and harvesting rate was resear-ched. Simultaneously, the optimal equilibrium and the optimal harvest policy are obtained by using stability analysis and Pontryagin’s maximal principle. As a result, this manuscript can supply a certain reference for the authorities... |
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