Dynamic analysis of a predator-prey diffusion model with fear effect and modification of Holling-Ⅱ(具有恐惧效应及修正的Holling-Ⅱ捕食者-食饵扩散模型的动力学分析)

Abstract

A Holling-Ⅱ predator-prey diffusion model with fear effect and modification under homogeneous Dirichlet boundary conditions is studied. Firstly, the prior estimation of the model is given by applying the maximum value principle and comparison theorem. Then, by calculating the fixed point index of the cone map, the sufficient condition for the existence of the positive solution is obtained. When H is sufficiently large, the stability of the positive solution is discussed according to the linear stability theory. Finally, by means of spectral analysis and branching theorem, the existence and stability of local branching solutions are discussed with m as the branching parameter.(研究了在齐次Dirichlet边界条件下一类具有恐惧效应及修正的Holling-Ⅱ捕食者-食饵扩散模型。首先，利用极大值原理和比较定理给出模型的先验估计；然后，通过计算锥映射不动点指标，得到正解存在的充分条件，且根据线性稳定性理论，讨论了当H充分大时正解的稳定性；最后，借助谱分析和分支定理，以m为分支参数，讨论了局部分支解的存在性与稳定性。)

Keywords

• fear effect(恐惧效应)
• modified holling-ⅱ functional response function(修正的holling-ⅱ功能反应函数)
• stability(稳定性)
• local branching solution(局部分支解)