【摘要】 应用生物数学理论研究生态平衡与可持续发展是生态系统的一个热门课题.在海洋渔业的捕捞过程中,既要保证生态平衡,又要使捕捞收益最大更是海洋渔业关注的重要课题.目前对离散系统的捕捞研究较少.运用离散差分方程的稳定性理论,讨论一类具有捕获的离散Leslic捕食-食饵种群的系统,获取正平衡点的局部渐近稳定的充分条件.通过构造适当的Liapunov函数,利用二元函数的泰勒展开式讨论正平衡点存在必全局稳定性的结果.利用函数的极值判定法讨论在维持稳定捕获前提下的最优捕获策略,来获取最优经济效益.最后,通过一个适当的例子及数值模拟的说明主要结果是合理的.给实际生产提供了理论依据,具有一定的指导意义.更多还原

【Abstract】 The application of biological mathematical theory to the studies of ecological balance and sustainable development is a hot topic of ecosystem.In marine fisheries catch process,not only is it necessary to ensure the ecological balance,but also to maximize the biggest fishing benefits,an important issue which marine fisheries concern the most.At present,there are few researches on the catch of small discrete systems.By applying the stability theory of discrete differential equations,we attempt to discuss the species with harvesting discrete Leslic predator-prey system and obtain the sufficient conditions of the existence and partial stability of positive equilibrium point.By constructing the Lyapunov function and employing the Taylor expanding of quadratic function,we find that if the positive equilibrium exists,the system is globally and asymptotically stable.With the extreme value method,we explore the optimal harvesting strategy under the premise of maintaining the stable harvesting so as to get the optimal economic returns.Finally,the feasibility of the main results is proved by one suitable example together with its numerical simulations.The findings can provide a theoretical basis and guidance significance for actual production.更多还原