| 一类带恐惧效应的三物种食物链模型的分支分析 |
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| 引用本文： | 王彩宇,常玉,陈晓楠.一类带恐惧效应的三物种食物链模型的分支分析[J].北京化工大学学报(自然科学版),2021,48(5):119-123. |
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| 作者姓名： | 王彩宇 常玉 陈晓楠 |
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| 作者单位： | 北京化工大学 数理学院, 北京 100029 |
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| 基金项目： | 国家自然科学基金（11771033） |
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| 摘 要： | 主要研究了恐惧效应对三物种食物链模型中分支动态的影响，运用中心流形定理和局部分支理论分析了Hopf分支、transcritical分支和saddle-node分支的存在性，并给出相应的数值模拟结果。研究结果表明，分支是种群发生失稳和周期性振荡的根本原因，从而揭示了恐惧效应是维持种群稳定的重要因素。
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| 关 键 词： | 中心流形 Hopf分支 transcritical分支 saddle-node分支 恐惧效应 |
| 收稿时间： | 2020-12-03 |
Bifurcation analysis of a model of a three-species food chain with a fear effect |
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| WANG CaiYu,CHANG Yu,CHEN XiaoNan.Bifurcation analysis of a model of a three-species food chain with a fear effect[J].Journal of Beijing University of Chemical Technology,2021,48(5):119-123. |
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| Authors: | WANG CaiYu CHANG Yu CHEN XiaoNan |
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| Institution: | College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China |
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| Abstract: | We have investigated the influence of fear effect on bifurcation dynamics in a three-species food chain model. The existence of Hopf bifurcation, saddle-node bifurcation and transcritical bifurcation were studied using the corresponding center manifolds and local bifurcation theory, and numerical simulation studies demonstrated various types of bifurcation. All these results indicate that bifurcation is the fundamental cause of population instability and periodic oscillations that occur, and that fear effects play an important role in maintaining population stability. |
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| Keywords: | center manifold Hopf bifurcation transcritical bifurcation saddle-node bifurcation fear effect |
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