一类食饵具有常数收获率和Holling第II类功能性反应的捕食者–食饵模型的分支分析
Bifurcation Analysis of a Predator-Prey Model with Constant Prey Harvesting Rate and Holling Type II Functional Response
摘要: 本文研究一类食饵种群具有常数收获率且有Holling第Ⅱ类功能性反应的捕食者–食饵模型的平衡点和分支问题。首先给出系统模型平衡点的存在条件，然后主要讨论了平衡点的类型及稳定性和正平衡点的Hopf分支，且得出了产生Hopf分支的条件；最后，对该模型做了数值仿真模拟实验得到了相关结论。
Abstract: In this paper, we study the equilibria and the bifurcation of a predator-prey model with constant prey harvesting rate and Holling type II functional response. Firstly, we analyze the existence condition of the equilibria of the system model. Then, we discuss the type and stability of the equilibria, Hopf bifurcation near positive equilibria and we obtain the conditions of Hopf bifurcation. Finally, the numerical simulation of the model is carried out and the relevant conclusions are obtained.
文章引用：陆秀琴, 温洁嫦. 一类食饵具有常数收获率和Holling第II类功能性反应的捕食者–食饵模型的分支分析[J]. 动力系统与控制, 2019, 8(4): 271-277. https://doi.org/10.12677/DSC.2019.84029

参考文献

[1] 马知恩. 种群生态学的数学建模与研究[M]. 合肥: 安徽教育出版社, 1996.
[2] Zhu, C.R. and Lan, K.Q. (2010) Phase Portraits, Hopf Bifurcation and Limit Cycles of Leslie-Gower Predator-Prey Systems with Harvesting Rates. Discrete and Continuous Dynamical Systems—Series B, 14, 289-306.
[Google Scholar] [CrossRef] 
[3] Gong, Y.J. and Huang, J.C. (2014) Bogdanov-Takens Bifurcation in a Leslie-Gower Predator-Prey Model with Prey Harvesting. Acta Mathematicae Applicatae Sinica, English Series, 30, 239-244.
[Google Scholar] [CrossRef] 
[4] 刘宣亮, 王志星. 一类捕食者有传染病的捕食者-食饵模型的分支分析[J]. 北华大学学报(自然科学版), 2018, 19(3): 281-290.
[5] 梁肇军, 陈兰荪. 食饵种群具有常数收获率的二维volterra模型的定性分析[J]. 生物数学报, 1986(1): 22.
[6] 傅仙发, 陈剑峰, 岳金健. 食饵带收获率的Holling-2型捕食者——食饵模型的Bautin分岔[J]. 长春师范大学学报, 2018, 37(12): 1-3.
[7] 张攀. Holling II型捕食者——食饵模型的稳定性和Hopf分支[J]. 洛阳理工学院学报(自然科学版), 2019(1): 83-85.
[8] Wang, X.Y., Zanette, L. and Zou, X.F. (2016) Modelling the Fear Effect in Predator-Prey Interactions. Journal of Mathematical Biology, 73, 1179-1204.
[Google Scholar] [CrossRef] [PubMed]
[9] Mukhopadhyay, B. and Bhattacharyya, R. (2016) Effects of Harvesting and Predator Interfererce in a Model of Two-Predators Competing for a Single Prey. Applied Mathematical Modelling, 40, 3264-3274.
[Google Scholar] [CrossRef] 
[10] 张芷芬, 丁同仁, 黄文灶, 董镇喜. 微分方程定性理论[M]. 北京: 科学出版社, 1985.
[11] 马知恩, 周义仓. 常微分方程定性与稳定性方法[M]. 北京: 科学出版社, 2007.
[12] Peng, R. and Wang, M. (2007) Global Stability of the Equilibrium of a Diffusive Holling-Tanner Prey-Predator Model. Applied Mathematics Letters, 20, 664-670.
[Google Scholar] [CrossRef] 
[13] Kuznetsov, Y.A. (1998) Elements of Applied Bifurcation Theory. 2nd Edition, Springer-Verlag, New York.

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