The Effects of Harvesting and Time Delay on Predator-prey Systems with Holling Type II Functional Response
The Effects of Harvesting and Time Delay on Predator-prey Systems with Holling Type II Functional Response
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DOI：
10.1137/080728512
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发表时间：
2009-09
期刊：
影响因子：
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通讯作者：
J. Xia;Zhihua Liu;R. Yuan;S. Ruan
中科院分区：
文献类型：
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作者：
J. Xia;Zhihua Liu;R. Yuan;S. Ruan
本文利用Faria和Magalhaes发展的时滞泛函微分方程范式理论，研究了捕食者特定增长时滞和时滞对两类捕食者-食饵系统的影响[J.Differtions，122(1995)，第181-200页，J.Differtions，122(1995)，pp.201-224]。以时滞为分支参数，在捕食者以恒定速度捕获的模型中证明了Hopf分支，并给出了支持我们理论预测的数值例子。此外，分歧分析表明，捕食者具有捕食者的时滞捕食系统存在Bogdanov-Takens分支。得到了模型在Bogdanov-Takens奇点下的横向展开，并给出了数值模拟和分岔图。
In this paper, the effects of harvesting and time delay on two different types of predator-prey systems with delayed predator specific growth and Holling type II functional response are studied by applying the normal form theory of retarded functional differential equations developed by Faria and Magalhaes [J. Differential Equations, 122 (1995), pp. 181–200, J. Differential Equations, 122 (1995), pp. 201–224]. Hopf bifurcations are demonstrated in models with harvesting of the prey at a constant rate by taking the delay as a bifurcation parameter, and numerical examples supporting our theoretical prediction are also given. Furthermore, bifurcation analysis indicates that delayed predator-prey systems with predator harvesting exhibit Bogdanov–Takens bifurcation. The versal unfoldings of the models at the Bogdanov–Takens singularity are obtained, and numerical simulations and bifurcation diagrams are given to illustrate the obtained results.