Mathematical Study On The Management Of Ecological Resources Model With Pulse Effect

In recent years, as the economy has developed and society progressed, terrestrial and marine ecosystems are destroyed seriously, and its immediate cause is the unreasonable development of natural resources. With the rapid expansion of mathematical biology , mathematical models are used to study more and more problems of ecological and natural resources. This dissertation bases on impulsive differential dynamical system, Firstly, acquisition and management models of Marine Fishery Resources are established which has a background of more and more serious offshore pollution. Secondly, taking environmental pollution and the waste of resources brought by chemical pesticides into consideration, reasonable pest management models are established.Firstly, we introduce the backgroud knowledge.In Chapter 1, recently, due to excessive exploitation of marine resources, the ocean resources extremely decline. More and more serious marine pollution (especially inshore marine pollution) brings great difficulty for marine resources management. In order to better manage and utilize the marine resources, in this chapter, we consider the effects of impulsive diffusion on the species in a polluted environment and investigate an inshore-offshore fishery model. The sufficient conditions are obtained for the existence of the positive periodic solution and the global asymptotic stability of both the trivial periodic solution and the positive periodic solution. Moreover, in a polluted environment, the optimal harvesting policy is given for the inshore subpopulation, which includes the maximum sustainable yield and the corresponding harvesting effort. Numerical simulations confirm our theoretical results.In Chapter 2, Concerning the polluted environment in inshore areaand the effects of unbalanced impulsive diffusion between inshore and offshore areas on the size of fish population, based on optimal harvesting policy, a logistic offshore fishery system with impulsive pollutant input in inshore area and impulsive diffusion at different fixed time is formulated, and we investigate the dynamics of such a system. The sufficient conditions are obtained for the existence of the positive periodic solution and the global asymptotic stability of both the trivial periodic solution and the positive periodic solution. Moreover, the maximum sustainable yield and the corresponding harvesting effort are obtained.In chapter 3 we establish a state-dependent pest management model which has a background of agricultural pest management. When the number of both larvae and adult has reached a dangerous level, the natural enemies are distributed, meanwhile the pesticides are sprayed. We researched the existence and attractivity of order one periodic solution by using semi-dynamical syetem and differential equation qualitative theory .Moreover, in the end of each chapter, by mathematical software such as Matlab and Maple we give some numeric simulation results which confirm the theoretical conclusions. Finally, we give an overall conclusion.