毒物作用下一类具有HollingⅡ型功能反应的捕食-食饵渔业模型及其最优收获  

Optimal Harvesting of a Prey-Predator Fishery Model with Holling TypeⅡ Functional Response in the Presence of Toxicity

作　　者：钟琪琪 韦煜明 彭华勤 ZHONG Qi-qi;WEI Yu-ming;PENG Hua-qin(School of Mathematics and Statistics,Guangxi Normal University,Guilin 541006,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：《南宁师范大学学报（自然科学版）》2022年第1期1-11,共11页Journal of Nanning Normal University：Natural Science Edition

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

摘　　要：该文研究采用独立捕捞策略和人为毒物非线性作用下,具有HollingⅡ型功能反应的捕食-食饵渔业模型的最优控制问题;在一定的限制条件下得到了平衡点的稳定性判据,讨论了非平凡共存平衡点的全局稳定性,并考虑了可能的生物经济平衡;在保持渔业资源可持续性的前提下,运用Pontryagin极大值原理确定了最优收获策略.最后用数值模拟验证了理论分析.This paper investigates an optimal control problem of a prey-predator fishery model with Holling typeⅡfunctional response,which is based on independent harvesting strategies and nonlinear effects of an anthropogenic toxicant.Under certain restrictions,we obtain the stability criteria of the equilibrium solutions,and then discuss the global stability of the non-trivial coexistence equilibrium solution.The bionomic equilibrium solutions for some possible cases is also considered.Optimal harvesting policy is established by utilizing the Pontryagin's Maximum Principle while maintaining the sustainability of the marine fishery resources.Finally,the above theoretical analysis is verified by numerical simulations.

关 键 词：捕食-食饵渔业模型 毒物 生物经济平衡 最优收获策略 

分 类 号：Q141[生物学—生态学] O175[生物学—普通生物学]