Abstract A prey-predator model incorporating prey refuge with variable carrying capacity and Holling type-II functional response is proposed and analyzed. The model includes a case of increasing carrying capacity as well as a decreasing carrying capacity case. Sufficient conditions are derived to ensure the existence and local stability of the equilibrium points of the proposed model. Moreover, the occurrence of transcritical bifurcation as well as Hopf bifurcation are investigated. The effect of some model parameter related to the prey refuge and the variable carrying capacity on the prey-predator dynamics has been examined. Numerical simulations are presented to demonstrate the theoretical results and to illustrate the effect of these parameters on the model dynamics. Moreover, a comparison with the constant carrying case has been presented.

中文翻译：

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包含可变承载能力的猎物避难所的猎物-捕食者模型的动力学分析

摘要 提出并分析了包含可变承载能力和Holling II型功能反应的猎物避难所的猎物-捕食者模型。该模型包括承载能力增加的情况以及承载能力下降的情况。推导出足够的条件来确保所提出模型的平衡点的存在和局部稳定性。此外，研究了跨临界分岔和Hopf分岔的发生。研究了与猎物避难所和可变承载能力相关的一些模型参数对猎物-捕食者动力学的影响。给出了数值模拟来证明理论结果并说明这些参数对模型动力学的影响。此外，还介绍了与固定手提箱的比较。