周期变化环境中一类尺度结构种群系统的最优控制  

Optimal Contraception Control for a Nonlinear Vermin Model with Size-Structure in a Periodic Environment

作　　者：刘荣 何泽荣[2] LIU Rong;HE Zerong(School of Applied Mathematics,Shanxi University of Finance and Economics,Taiyuan 030006;Institute of Operational Research and Cybernetics,Hangzhou Dianzi University,Hangzhou 310018)

机构地区：[1]山西财经大学应用数学学院,太原030006 [2]杭州电子科技大学运筹与控制研究所,杭州310018

出　　处：《系统科学与数学》2022年第8期1973-1989,共17页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(12001341,11871185);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)资助课题。

摘　　要：研究一类周期环境中具有尺度结构的非线性害鼠不育控制模型,其中控制变量同时出现在主方程和边界条件.首先利用冻结系数法和不动点理论证明模型非负解的存在唯一性,并给出状态关于控制变量的连续依赖性.接着利用共轭系统和切-法锥技巧导出最优性条件,再运用Ekeland变分原理证明最优不育策略的存在性.最后给出数值模拟结果,它表明:降低害鼠的繁殖率相对于增加其死亡率是预防鼠害发生的一种更为有效的方式.In this paper,we investigate a periodic nonlinear size-structured vermin model with contraception control,in which the control variable appears in the principal equation and the boundary condition as well.Firstly,we establish the existence of a unique non-negative solution by means of frozen coefficients and fixed point theory,and show the continuous dependence of solutions on control variable.Next,adjoint system and tangent-normal cone techniques are used to obtain the optimality conditions.The existence of optimal contraception policy is verified by means of Ekeland's variational principle.Finally,some numerical results are presented,which shows that reducing the reproduction rate of the vermin is more effective than increasing its mortality to ease damages.

关 键 词：不育控制 尺度结构 周期环境 害鼠模型 

分 类 号：R184.35[医药卫生—流行病学] O232[医药卫生—公共卫生与预防医学]