污染环境下具有强Allee效应的食饵-捕食系统收获策略  

Harvesting Strategies for Predator⁃prey Systems with Strong Allee Effects in Contaminated Environments

作　　者：钟颖 韦煜明 彭华勤 ZHONG Ying;WEI Yuming;PENG Huaqin(College of Mathematics and Statistics,Guangxi Normal University,Guilin 541004,China)

机构地区：[1]广西师范大学数学与统计学院,广西桂林541006

出　　处：《广西民族大学学报（自然科学版）》2023年第1期72-81,共10页Journal of Guangxi Minzu University ：Natural Science Edition

基　　金：国家自然科学基金项目(11961074,12061016,12001125);广西自然科学基金项目(2018GXNSFBA281140,2018GXNSFAA294084)。

摘　　要：研究了外界环境被污染的情况下,具有Allee效应和Holling-Ⅱ型功能反应函数的食饵-捕食模型的收获策略。首先讨论了该系统平衡点的稳定性,其次利用Liapunov函数证明了正平衡点的全局稳定性,然后讨论系统的生物经济平衡的存在性,用Pontryagin's最大值原理探讨了最优收获策略,最后利用数值模拟解释这些结果。The harvesting strategy of a prey⁃predator model with Allee effect and Holling⁃Ⅱtype functional response function under the contaminated external environment is investigated.Firstly,the stability of the equilibrium point of the system is discussed,secondly,the global stability of the positive equilibrium point is proved using the Liapunov function,then the existence of the bioeconomic equilibrium of the system is examined,the optimal harvesting strategy is explored using Pontryagin's maximum principle,and finally,these results are explained using numerical simulations.

关 键 词：食饵-捕食系统 毒物 Allee Holling-Ⅱ型 最优收获策略 

分 类 号：O175[理学—数学]