Single Population Best Capture Strategy

The optimal management of renewable resources, which has a direct relationship to sustainable development and exploitation has come into the problems concerned by ecologists and economists and has been taken count of by academic field. In [1-5], many single-species harvesting models were discussed. In [6][7], persistence and global asymptotic behavior in single-species ecological system were studied. In [8-14], some optimal harvesting models of growth in biology were discussed. The optimal harvesting policies that maximized the sustainable yield for nonautonomous single-species harvesting models, which had a unique globally asymptotically stable periodic solution, were obtained by Fan Meng [15] and Li Hailong [16]. In [17-20], some single-species models of growth were given. In [21-25], the optimal harvesting policies for autonomous single-species harvesting models were studied, which maximized the sustainable yield and economic rent respectively. In [26-30], the optimal harvesting policies that maximized the sustainable yield for autonomous single-species harvesting models were studied.Presently, almost all optimal harvesting policies were obtained by choosing production function that was separable of variables concerning x and E and was independent of time t. This is not completely consistent with the objective facts. As a matter of fact, situation is complicate, and it is not necessarily the case that production function is separable of variables concerning x or E and does not vary with time t. In this paper, production function is more extensive than those of literature on hand. Furthermore, we generalize the growth equation. Hence, it is not easy to find the optimal harvest effort for our generalized models. In this paper, using a new method, we discuss the optimal harvesting problems of single-species biological resource. We choose the maximum sustainable yield and net revenue as the management objectives and investigate the optimal harvesting policies for a class of single-species models. Our results include almost all single-species models researched in literatures.The organization of the paper is as follows: ?. 1 the autonomous single-species harvesting model that carry general nature we consider is given and production function that is separable of variables concerning xand E become the application of this paper; . 2 We Choose the maximum sustainable yield as the management objective; We Choose the maximum sustainable economic rent as the management objective in . 3;?. 4 Some applications are given and some results are generalized.?. 1 the nonau-tonomous single-species harvesting model with periodic coefficients we study is given ?. 2 we investigate global asymptotic stability of the syste; ?. 3 we choose unit time the maximum sustainable yield as the management objectie; ?. 4 Application.