Scholarlink

<p>In this paper, the dynamic properties of a predator–prey model with Holling IV functional response and Michaelis–Menten type harvesting are discussed. Our study reveals that, under the supposition that both prey and predator evolve on a single time scale, the highest codimension of a nilpotent cusp is 4. It is also demonstrated that in this case the model is able to undergo the degenerate Bogdanov–Takens bifurcation of codimension 4. The present study also employs the geometric singular perturbation theory and blow-up technique to demonstrate a series of complex dynamics of the slow–fast system for this model. These dynamics include relaxation oscillation, singular Hopf bifurcation, singular Bautin bifurcation and singular Bogdanov–Takens bifurcation. Moreover, numerical simulations are conducted in order to provide supporting evidence for the theoretical findings.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Singular Bogdanov–Takens bifurcation of a predator–prey system with Holling IV functional response and harvesting

  • 期刊论文

  • 发表日期：

    2026年7月8日

查看全文
  • Qinghui Ma,
  • Yue Zhang

摘要

In this paper, the dynamic properties of a predator–prey model with Holling IV functional response and Michaelis–Menten type harvesting are discussed. Our study reveals that, under the supposition that both prey and predator evolve on a single time scale, the highest codimension of a nilpotent cusp is 4. It is also demonstrated that in this case the model is able to undergo the degenerate Bogdanov–Takens bifurcation of codimension 4. The present study also employs the geometric singular perturbation theory and blow-up technique to demonstrate a series of complex dynamics of the slow–fast system for this model. These dynamics include relaxation oscillation, singular Hopf bifurcation, singular Bautin bifurcation and singular Bogdanov–Takens bifurcation. Moreover, numerical simulations are conducted in order to provide supporting evidence for the theoretical findings.