周期环境中捕食者具有尺度结构的三物种捕食-食饵系统的最优收获  

Optimal Harvesting in a Periodic 3-Species Predator-Prey Model With Size Structure in Predators

作　　者：刘荣 刘桂荣[2] LIU Rong;LIU Guirong(School of Applied Mathematics,Shanxi University of Finance and Economics,Taiyuan 030006,P.R.China;School of Mathematical Sciences,Shanxi University,Taiyuan 030006,P.R.China)

机构地区：[1]山西财经大学应用数学学院,太原030006 [2]山西大学数学科学学院,太原030006

出　　处：《应用数学和力学》2021年第5期510-521,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(12001341,11971279);山西省青年科技研究基金(201901D211410);山西省高等学校科技创新项目(2020L0258)。

摘　　要：对种群动力学及相关控制问题的研究,不仅具有理论意义,而且与生物多样性保护、病虫害防治及可再生资源的开发利用密切相关.该文研究了一类周期环境中具有两相互竞争食饵和一捕食者的三物种捕食-食饵系统的最优收获,其中捕食者具有尺度结构且用一阶偏微分方程描述.运用不动点定理证明了系统非负有界解的存在唯一性,并讨论了解关于控制变量的连续依赖性.应用切-法锥技巧导出最优收获条件,并借助Ekeland变分原理讨论了最优策略的存在唯一性.这里目标泛函表示收获三物种产生的净经济效益.所得结果将有利于可再生资源的开发.The research on population dynamics and related control problems is not only of theoretical significance,but also closely related to biodiversity protection,pest control,and the development and utilization of renewable resources.The optimal harvesting problem was considered in a periodic 3-species predator-prey system with 1 predator and 2 competing preys,where the predator has size structure and was described with 1 st-order partial differential equations.First,the existence of a unique non-negative solution of the controlled system was proven by means of the fixed-point reasoning,and the continuous dependence of the solution on the control variables was discussed.Then,the optimal harvesting conditions were given with the techniques of tangential-normal cones and the adjoint system.Finally,with Ekeland’s variational principle,the existence of the optimal harvesting strategy was derived.Here the objective functional represents the net economic benefit in the harvesting of 3 species.The results obtained would be beneficial for exploration of renewable resources.

关 键 词：周期环境 尺度结构 三物种 捕食-食饵 最优收获 

分 类 号：O175.22[理学—数学]