基于出生率控制且依赖尺度结构的食饵种群的最优收获  

Optimal Harvest of Prey Population Based on Scale Structure of Birth Rate Control

作　　者：张萍 卢广西 ZHANG Ping;LU Guangxi(Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《洛阳理工学院学报（自然科学版）》2020年第4期81-86,共6页Journal of Luoyang Institute of Science and Technology：Natural Science Edition

摘　　要：在控制出生率的情况下,建立了一类依赖于尺度结构的食饵种群模型。首先利用不动点定理证明该系统存在唯一的解,然后通过细致严密的理论分析推得解对控制变量的连续依赖性,最后推导出共轭系统并从法锥的特征结构出发导出收获控制为最优的必要性条件。In the case of birth rate control,a prey population model is built depend on the scale structure.First,it is proved thatthe uniqueness of non-negative solutions of conjugate system exists by using fixed point theorem.Besides,the continuous dependence of the control variables is concluded.Finally,by means of cutting cone method,the characteristics of cone structure to the optimumconditions is deduced.

关 键 词：适定性 共轭系统 最大值原理 

分 类 号：O175.1[理学—数学]