毒素影响下具有避难所的捕食-食饵系统的最优收获  

Optimal harvesting analysis of a predator-prey system with prey refuge in presence of toxicity

作　　者：王琼燕 赵春[1] WANG Qiongyan;ZHAO Chun(College of Mathematical Science,Tianjin Normal University,Tianjin 300387,China)

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《天津师范大学学报（自然科学版）》2018年第5期14-19,共6页Journal of Tianjin Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11271104)

摘　　要：研究一类毒素影响下具有避难所的捕食-食饵系统的最优收获问题.利用Jacobi矩阵的特征值和构造恰当的Lyapunov函数,证明了系统平衡点的局部稳定性和全局稳定性,并利用Pontryagin最大值原理得到了达到最优收获的平衡解.The optimal harvesting problem for a predator-prey system with prey refuge in the presence of toxicity is studied.By using the characteristic value of Jacobi matrix and constructing appropriate Lyapunov function,the local stability and global stability of equilibrium point of the system are proved. Moreover,the equilibrium solution of optimal harvesting is obtained by using the Pontryagin′s maximal principle.

关 键 词：捕食-食饵系统 避难所 毒素 稳定性 最优收获 

分 类 号：O232[理学—运筹学与控制论]