Scholarlink

<p>The predator–prey model is described by logistic differential equations, which capture the evolutionary dynamics of species. Incorporating multiple factors into predator–prey dynamics remains a critical and unresolved challenge in ecological modeling. In this paper, we propose a fractional-order predator–prey model based on prey logistic growth, incorporating the fear effect on prey, immigration factors, and cannibalism among predators. To account for memory effects, we apply two distinct fractional differential operators: the Caputo fractional derivative characterized by a power-law kernel, and the Atangana–Baleanu fractional derivative in the Caputo sense (ABC) characterized by a Mittag–Leffler kernel. We analyze the existence and uniqueness of solutions for the corresponding models under the Caputo sense and the ABC sense. For the model with the Caputo sense, we further examine the local and global stability of relevant equilibrium points and establish the conditions for the existence of Hopf bifurcations. Our results demonstrate that the Atangana–Baleanu derivative in Caputo (ABC) sense exhibits greater convergence of solutions compared to the Caputo fractional order. Numerical simulations reveal that the fear effect plays a stabilizing role in this model, while an increase in immigration factors tends to heighten instability. Additionally, the phenomenon of cannibalism can facilitate the persistence of species that are otherwise destined for extinction.</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

Dynamic analysis of predator–prey model with fear, cannibalism, and prey immigration using caputo and ABC fractional derivatives

  • 期刊论文

  • 发表日期：

    2025年6月14日

查看全文
  • Lei Yang,
  • Wanmin Feng,
  • Minxuan Zhang,
  • Tiegang Zhang

摘要

The predator–prey model is described by logistic differential equations, which capture the evolutionary dynamics of species. Incorporating multiple factors into predator–prey dynamics remains a critical and unresolved challenge in ecological modeling. In this paper, we propose a fractional-order predator–prey model based on prey logistic growth, incorporating the fear effect on prey, immigration factors, and cannibalism among predators. To account for memory effects, we apply two distinct fractional differential operators: the Caputo fractional derivative characterized by a power-law kernel, and the Atangana–Baleanu fractional derivative in the Caputo sense (ABC) characterized by a Mittag–Leffler kernel. We analyze the existence and uniqueness of solutions for the corresponding models under the Caputo sense and the ABC sense. For the model with the Caputo sense, we further examine the local and global stability of relevant equilibrium points and establish the conditions for the existence of Hopf bifurcations. Our results demonstrate that the Atangana–Baleanu derivative in Caputo (ABC) sense exhibits greater convergence of solutions compared to the Caputo fractional order. Numerical simulations reveal that the fear effect plays a stabilizing role in this model, while an increase in immigration factors tends to heighten instability. Additionally, the phenomenon of cannibalism can facilitate the persistence of species that are otherwise destined for extinction.