模拟周期环境和年龄等级结构的种群系统的最优收获策略  

Optimal Harvesting for a Population System Modelling Periodic Environment and Hierarchical Age-Structure

作　　者：刘荣 张凤琴 LIU RONG;ZHANG FENG-QIN(School of Applied Mathematics,Shanci University of Finance and Economics,Taiyuan 030006,China;School of Mathematics and Information Technology,Yuncheng University,Yuncheng 044000,China)

机构地区：[1]山西财经大学应用数学学院,太原030006 [2]运城学院数学与信息技术学院,运城044000

出　　处：《应用数学学报》2025年第1期33-52,共20页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(12071418,12001341)资助项目。

摘　　要：研究一类周期环境中基于个体年龄等级结构的种群系统的最优收获问题.首先,应用冻结系数法和不动点理论得到状态系统非负有界周期解的存在唯一性,及共轭系统的适定性.其次,利用共轭系统和法锥技巧导出最优收获策略的结构,运用Ekeland变分原理证明最优收获策略的存在唯一性.最后,通过数值模拟验证理论结果的有效性的同时发现系统的其他动力学性质.本文的结果推广和改进了相关文献的部分结果.Ecological researches show that there exist dominance ranks of individuals in many species.Moreover,natural populations are actually subject to seasonal fuctuations which makes their habitats often undergoes some periodic changes.Motivated by these considerations,in this paper,we investigate the optimal harvesting problem for a hierarchical age-structured population system in a periodic environment.Here the objective functional represents the net economic benefit yielded from harvesting.Firstly,by means of frozen coefficients and fixed point theory we show that the state system is well posed if the reproducing number is less than one.Meanwhile,it is shown that the population density depends continuously on control parameters.Similarly,we show that the adjoint system is also well posed.Then,the optimality conditions given by the feedback forms of state variable and adjoint variable are obtained by using the adjoint system and tangent-normal cone techniques.The existence of optimal harvesting policy is verified via Ekeland's variational principle and fixed point reasoning.Finally,we use numerical simulations to verify the main results and find other dynamic properties of the system.The results in this paper generalize and improve the previous related results.

关 键 词：周期环境 年龄等级 最优收获 谱半径 最大值原理 

分 类 号：O212.7[理学—概率论与数理统计]