广义Richards-Gilpin-Ayala模型的捕获优化问题

Optimal Harvesting Problem for Generalized Richards-Gilpin-Ayala Model

在Richards-Gilpin-Ayala模型的基础上,提出了一类更广泛的数学模型—广义Richards-Gilpin-Ayala模型.进而讨论该模型单种群生物资源的捕获优化问题,分析了被开发生物种群的动力学性质.在单位捕获努力量假定下,以最大可持续捕获量为管理目标,确定了线性捕获下的最优捕获策略,得到了最优捕获努力量,最大可持续收获及相应的最优种群水平的显式表达式.这些结果推广了相关文献中关于Schaefer模型、广义Logistic模型的相应结果.

This paper is devoted to the study of the optimal harvesting problem for single population based on the generalized Richards-Gilpin-Ayala model which proposed by the author. First, we analyze the dynamical behaviour of the harvested population. Then under the catch-per-unit-effort hypothesis, we choose the maximum sustainable yield as the management objective, and investigate the optimal harvesting policies for the generalized Richards-Gilpin- Ayala model. Explicit expressions are obtained for the optimal harvest effort that maximizes the sustainable yield, the corresponding optimal population level, and the maximum sustainable yield. These results generalize the known results for Schaefer model and generalized Logistic model in renewable resources management.