Periodic solution and control optimization of a prey-predator model with two types of harvesting

被引：42
作者：
Wang, Jianmei [1 ]
Cheng, Huidong [1 ]
Liu, Hongxia [1 ,2 ]
Wang, Yanhui [1 ,2 ]
机构：
[1] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao, Peoples R China
[2] Shandong Univ Sci & Technol, State Key Lab Min Disaster Prevent & Control Shan, Qingdao, Peoples R China
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2018年
基金：
中国国家自然科学基金;
关键词：
prey-predator model; state-dependent impulse; order-1 periodic solution; optimization; stability; DYNAMICS ANALYSIS; HOMOCLINIC BIFURCATION; NONLINEAR PULSE; GLOBAL DYNAMICS; SYSTEM; STABILITY; DELAY;
D O I：
10.1186/s13662-018-1499-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work, a prey-predator model with both state-dependent impulsive harvesting and constant rate harvesting is investigated, where the replenishment rate of prey and the harvesting rate are linearly related with the selected threshold. By first using the successor function method and differential equation geometry theory, the existence, uniqueness and asymptotic stability of the order-1 periodic solution are discussed. And then numerical simulations with an example are given to illustrate the feasibility of the theorem-related results. Moreover, in order to increase the total profit, the optimization strategy is presented and the optimal threshold is obtained.
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页数：14
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