Global analysis of a Holling type II predator–prey model with a constant prey refuge
Global analysis of a Holling type II predator–prey model with a constant prey refuge
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DOI：
10.1007/s11071-013-1157-4
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发表时间：
2014-04
影响因子：
5.6
通讯作者：
Guangyao Tang;Sanyi Tang;R. Cheke
中科院分区：
文献类型：
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作者：
Guangyao Tang;Sanyi Tang;R. Cheke
给出了一类食饵避难所为常数的Holling II型捕食模型的全局分析。虽然人们对该模型进行了大量的研究，但到目前为止，还没有得到唯一内部平衡点全局稳定的阈值条件及其极限环的唯一性。在这里，我们提供了一个全局定性分析来确定模型的全局动力学。特别地，结合Bendixson-Dulac定理和Lyapunov函数方法来判断平衡点的全局稳定性。利用线性系统极限环的唯一性定理证明了该模型极限环的存在唯一性。在此基础上，通过灵敏度分析讨论了捕食者避难所和参数空间对阈值条件的影响。在讨论中还讨论了基于不连续(或不连续)的盖斯捕食者-猎物模型的其他有趣的话题。
A global analysis of a Holling type II predator–prey model with a constant prey refuge is presented. Although this model has been much studied, the threshold condition for the global stability of the unique interior equilibrium and the uniqueness of its limit cycle have not been obtained to date, so far as we are aware. Here we provide a global qualitative analysis to determine the global dynamics of the model. In particular, a combination of the Bendixson–Dulac theorem and the Lyapunov function method was employed to judge the global stability of the equilibrium. The uniqueness theorem of a limit cycle for the Lineard system was used to show the existence and uniqueness of the limit cycle of the model. Further, the effects of prey refuges and parameter space on the threshold condition are discussed in the light of sensitivity analyses. Additional interesting topics based on the discontinuous (or Filippov) Gause predator–prey model are addressed in the discussion.