具有恐惧效应和 Beddington - DeAngelis 功能反应的时空共位群内捕食模型的稳定性和分叉分析

doi:10.12677/PM.2022.1212225

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具有恐惧效应和 Beddington - DeAngelis 功能反应的时空共位群内捕食模型的稳定性和分叉分析
Stability and Bifurcation Analysis of a Spatiotemporal Intraguild PredationModel with Fear Effect and Beddington-DeAngelis Functional Response

DOI: 10.12677/PM.2022.1212225, PDF, HTML, 下载: 186 浏览: 1,357 国家自然科学基金支持
作者: 王小宁：西北师范大学数学与统计学院，甘肃兰州
关键词: 共位群内捕食模型；Beddington - DeAngelis 型功能反应；恐惧效应；稳定性；Hopf 分支；Intraguild Predation Model； Beddington-DeAngelis Functional Response； Fear Effect； Stability； Hopf Bifurcation

摘要: 竞争和捕食是生态学中经常出现的一种现象，当两物种争夺相同的有限资源时，捕食者和食饵的共存是维持捕食者-食饵系统所必需的。研究共位群内捕食者和食饵在争夺同一资源时是否可能共存时非常有意义的。本文研究了具有恐惧效应的时空共位群内捕食模型的稳定性与Hopf 分支，该模型包含了以Beddington-DeAngelis 功能反应为特征的物种相互干扰，导出了共位群内捕食和食饵共存的条件，这是通过讨论平衡点的存在性，局部和全局渐近稳定性以及一致持久性来实现，其中平衡点的稳定性的条件是通过李雅普诺夫和赫尔维兹判据获得的。最后，我们以恐惧因子为分支参数，得到了各平衡点处Hopf 分支存在的条件。

Abstract: Competition and predation are a common phenomenon in ecology. When two species compete for the same limited resources, the coexistence of predator and prey is necessary to sustain the predator-prey system. It is of great significance to study whether predators and prey can coexist in a intraguild predation model when competing for the same resource. In this paper, we study the stability and Hopf bifurcation of a spatiotemporal intraguild predation model with a fear effect, the conditions for the coexistence of predator and prey in a intraguild predation model are derived by discussing the existence of equilibrium points, local and global asymptotic stability and uniform persistence, the condition of stability of equilibrium point is obtained by Lyapunov method and Helvetz criterion. Finally, we take the fear factor as the branching parameter and obtain the conditions for the existence of Hopf bifurcation at each equilibrium point.

文章引用：王小宁. 具有恐惧效应和 Beddington - DeAngelis 功能反应的时空共位群内捕食模型的稳定性和分叉分析[J]. 理论数学, 2022, 12(12): 2081-2105. https://doi.org/10.12677/PM.2022.1212225

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