Scholarlink

<p>In this work, we consider a two-dimensional Leslie–Gower prey–predator model with Allee effect to study system dynamics under multi-factor coupling. Firstly, to study the nature of the solution, we transform the established model to meet the Lipschitz condition. We further prove the positivity and boundedness of solutions for the system, and discuss the existence of positive equilibrium points. In addition, a separate analysis of the singular point (0,0) is made. Secondly, under the premise that the equilibrium point exists, we analyze the stability by the linearization method. Thirdly, we analyze the existence of some bifurcations of the system, including saddle-node bifurcation, Bogdanov–Takens bifurcation of codimension 2 and Hopf bifurcation. In the study of Hopf bifurcation without time delay, we calculate the Lyapunov number to determine the direction of the bifurcation. For Hopf bifurcation with time delay, we focus on the conditions for stability switch. Finally, in the numerical simulation, the results suggest that populations do not become extinct when the weaker Allee effect occurs, but instead help increase the persistence of predator and prey coexistence. The increase of the time delay of environmental carrying capacity on the population density will cause the unstability of the system, and even stability switch and other phenomena.</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

Complex dynamics analysis of an ecological model with Allee effect and time delay

  • 期刊论文

  • 发表日期：

    2025年4月19日

查看全文
  • Shuling Shen,
  • Li Miao,
  • Yi Zhang,
  • Linhe Zhu

摘要

In this work, we consider a two-dimensional Leslie–Gower prey–predator model with Allee effect to study system dynamics under multi-factor coupling. Firstly, to study the nature of the solution, we transform the established model to meet the Lipschitz condition. We further prove the positivity and boundedness of solutions for the system, and discuss the existence of positive equilibrium points. In addition, a separate analysis of the singular point (0,0) is made. Secondly, under the premise that the equilibrium point exists, we analyze the stability by the linearization method. Thirdly, we analyze the existence of some bifurcations of the system, including saddle-node bifurcation, Bogdanov–Takens bifurcation of codimension 2 and Hopf bifurcation. In the study of Hopf bifurcation without time delay, we calculate the Lyapunov number to determine the direction of the bifurcation. For Hopf bifurcation with time delay, we focus on the conditions for stability switch. Finally, in the numerical simulation, the results suggest that populations do not become extinct when the weaker Allee effect occurs, but instead help increase the persistence of predator and prey coexistence. The increase of the time delay of environmental carrying capacity on the population density will cause the unstability of the system, and even stability switch and other phenomena.