The Optimal Pulse Of The Biological Resources Development Strategy

The optimal exploitation and utilization of biologic resources, has much significance to study, and many authors have studied this problem, for example [2-4,7,15,17,19-22,24-31,34-37,41,42,45,47,48,51,54-63]. However, most of them only considered the case of continuous exploitation for resources. If the period of development is far more than the interval between two harvest moments, this supposition is reasonable and representative. For some exploitation in a short period, however, the supposition of continuous harvest has some doubt. Especially, for exploitation of fish or forest, due to growth period of these resources, developers have to harvest with pulse. Therefore, it is necessary to study sustainable development of biologic resources under supposition of impulsive harvest.Not only have impulsive systems signigicance for exploitation of biologic resources, in fact, but they also are fit for all social living, since lots of stochastic factors and distant fluctuation. Thus the theory of impulsive differential equations has been great developed [5,6,8-10,13,14,16,18,23,32, 33,38,39,43,44,46,50,52,53,65,67,68]. It is necessary to deal with realize problem using impulsive method. For example, for exploitation of resources, we can consider impulsive harvest instead of continuous harvest. Svetoslav I. Nenov first studied optimal n-impulsive harvest policy for general single population [49]. Xiaoying Zhang etc. studied existence and uniqueness of impulsive periodic solution for impulsive harvesting Logistic equation [64].In this paper, using different method, we study optimal n-impulsive harvest policies for general population, namely, during fixed time interval, maximize the population level at terminal moment of time interval, given fixed times impulsive harvest with constant quantity. Based the conclusion of the optimal problem, we give the concept of the sequence of F-optimal harvest moments. In section 3, we study gerenal optimal harvest policies byIVcanceling supposition of fixed constant quantity for each impulsive harvest. The new optimal problem change to maximize total impulsive harvest during fixed time interval with fixed times impulsive harvest. For these two optimal problems, we both consider realize application and further study direction.