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  

Dynamic analysis of a predator-prey diffusion model with fear effect and modification of HollingⅡ

作　　者：刘宇鹏 曹倩 包雄雄 LIU Yupeng;CAO Qian;BAO Xiongxiong(School of Science,Chang'an University,Xi'an 710064,China)

机构地区：[1]长安大学理学院,陕西西安710064

出　　处：《浙江大学学报（理学版）》2024年第2期186-195,共10页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(12101075);长安大学研究生科研创新实践项目(300103723070)。

摘　　要：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。A Holling-Ⅱpredator-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.

关 键 词：恐惧效应 修正的Holling-Ⅱ功能反应函数 稳定性 局部分支解 

分 类 号：O175.26[理学—数学]