一类具有Holling-II型功能反应的食饵带恐惧效应与捕食者非线性收获的捕食者-食饵模型的动力学性态
Dynamics of a Class of Prey-Predator Interaction Model with Holling Type-II Functional Response Incorporatingthe Effect of Fear on Prey and Non-Linear Predator Harvest
DOI: 10.12677/AAM.2024.137287, PDF, 下载: 7  浏览: 15 
作者: 李立：西北师范大学数学与统计学院，甘肃 兰州
关键词: Holling-II 型功能反应；平衡点；稳定性；Hopf分支；恐惧效应；Turing不稳定性；Holling-II Type Functional Response； Equilibrium； Stability； Hopf Branch； Fear Effect； Turing Instability
摘要: 本文研究了具有Holling-II型功能反应的捕食者-食饵模型的恐惧效应和对捕食者种群的非线性收获。对捕食者种群的恐惧增强了食饵种群的生存率，同时也大大减少了食饵种群的繁衍。对捕食者种群的捕获不仅可以获取经济收益，还可以调节捕食者与食饵的数量关系。文中研究了所有的生物可行平衡点并分析了可行平衡点的稳定时的模型参数。分析上，我们选择以捕食者种群的转化率为分支参数。模型系统经历了跨伍界分支，鞍结分支和Hopf分支。考虑捕食者和食饵种群在时空内的扩散效应，接着研究了正平衡点的局部稳定性，正平衡点和分支周期解的Turing不稳定性，Hopf分支的方向和分支周期解的稳定性。
Abstract: In this paper, we investigate the effects of fear effect and nonlinear predator harvest in predator-prey interaction models with Holling-II type functional response. Fear of the predator population increases the survival rate of the prey population and also greatly reduces the birth rate. The capture of the predator population can not only obtain economic benefits, but also regulate the quantitative relationship between predator and prey. In this paper, all viable equilibrium points are studied and the model parameters of stability of stability of viable equilibrium points are analyzed. In analysis, we have established that the conversion rate of predator population is the branch parameter and the model system undergoes transcritical branch, saddle- node branch and Hopf branch. Considering the diffusion effect of predator and prey population in space and time, we study the local stability of the positive equilibrium point, the positive equilibrium point and the Turing of the branch periodic solution instability, the direction of the Hopf branch and stability of the periodic solution of the branch.
文章引用：李立. 一类具有Holling-II型功能反应的食饵带恐惧效应与捕食者非线性收获的捕食者-食饵模型的动力学性态[J]. 应用数学进展, 2024, 13(7): 3015-3030. https://doi.org/10.12677/AAM.2024.137287

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