Harvesting of a predator–prey model with reserve area for prey and in the presence of toxicity

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• 作者：Hang Yang ; Jianwen Jia
• 关键词：Predator–prey system ; Toxicity ; Equilibria ; Stability ; Optimal harvesting policy
• 刊名：Journal of Applied Mathematics and Computing
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：53
• 期：1-2
• 页码：693-708
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theory of Computation; Mathematics of Computing;
• 出版者：Springer Berlin Heidelberg
• ISSN：1865-2085
• 卷排序：53

文摘

In this paper, we propose and investigate a predator–prey model with harvesting and reserve area for prey in the presence of toxicity. We research the boundedness of the solutions and the existence of the equilibria of this system. By analyzing the characteristic equations, the local asymptotically stability of feasible equilibria is discussed. By use of Lyapunov function method, we also obtain some sufficient conditions for globally stability of these equilibria. The optimal harvesting policy are discussed by using the Pantryagin’s maximum principle. Finally, numerical simulations are carried to verify the theoretical conclusions.