Study Of The Population Dynamics On The Protection Of The Giant Panda

In this paper, some differential equation models for describing the development of the giant panda population were established by dynamic modeling methods, and the dynamical behaviors of the differential systems were explored by impulsive differential equations theory, delay differential equations theory and other mathematical theories and numerical simulation methods. The results can be used to predict and infer the persistence of the giant panda population, and also provide theoretical basis for the study of giant panda protection. The results are summarized as follows.(1) An impulsive differential system on the relation of giant panda and two kinds of staple food bamboo was established, and how the staple food of bamboo flowering impact on the survival of the giant panda was discussed. Based on the investigation data of Wolong nature protection five one shed area, the relation between pandas and two kinds of staple food bamboo (Fargesia robusta and Bashania fargesii) was discussed by using numerical simulation method. The model can be used to consider whether bamboo flowering cause giant pandas to food shortages or not in some areas, and the study also provides a theoretical basis for blossom bamboo artificial regeneration and the artificial forest.(2) From the view of mathematics, a mathematical delay differential equation model of the relation between the trees, bamboo and giant pandas was established. Through the analysis of the variable coefficient differential systems with time delay and stage structure, the conditions for the permanence of the system were obtained, which can ensure the three populations to develop Corporately. The characteristics of this part are to verify the stability of the forest, bamboo and panda three-in-one system maintenance mechanism which was presented by Juqing Li et al. and to analyze the factors that restrict the stable development of the system, which will provide theoretical basis for the giant panda habitat protection.(3) An n dimensional differential system was established on the giant panda population dispersal in complex patchy environments. By mathematical analysis of the periodic coefficient diffusion differential system, sufficient conditions for permanence and extinction were obtained. Furthermore, the conclusions were applied to the local population in Qinling Mountains. The research method can be used to predict the future development of the local population of giant pandas.(4) Two mathematical models of release captive giant pandas in patchy environments were established, and the release mode of captive giant pandas was discussed by using state feedback control impulsive differential equations. Using the geometry theory of semi-continuous dynamical system, the existence and stability of order k periodic solutions in the phase space were studied. Thus, a series of release modes of the captive giant pandas were presented, for increasing small isolated pandas in patchy environments. Also, it would reintroduction wild pandas in the history of the giant panda distribution area.