阿利效应
数学
霍普夫分叉
博格达诺夫-塔肯分岔
分叉
简并能级
干草叉分叉
分岔图
应用数学
余维数
数学分析
控制理论(社会学)
非线性系统
物理
人口
计算机科学
控制(管理)
人口学
量子力学
社会学
人工智能
作者
Yingzi Liu,Zhong Li,Mengxin He
出处
期刊:Mathematical Biosciences and Engineering
[American Institute of Mathematical Sciences]
日期:2023-01-01
卷期号:20 (5): 8632-8665
摘要
<abstract><p>In this paper, we analyze the bifurcation of a Holling-Tanner predator-prey model with strong Allee effect. We confirm that the degenerate equilibrium of system can be a cusp of codimension 2 or 3. As the values of parameters vary, we show that some bifurcations will appear in system. By calculating the Lyapunov number, the system undergoes a subcritical Hopf bifurcation, supercritical Hopf bifurcation or degenerate Hopf bifurcation. We show that there exists bistable phenomena and two limit cycles. By verifying the transversality condition, we also prove that the system undergoes a Bogdanov-Takens bifurcation of codimension 2 or 3. The main conclusions of this paper complement and improve the previous paper <sup>[<xref ref-type="bibr" rid="b30">30</xref>]</sup>. Moreover, numerical simulations are given to verify the theoretical results.</p></abstract>
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