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<p>In this paper, we discuss a three-dimensional food web system that incorporates antipredator behavior. Previous studies have included the existence and local stability of the boundary equilibria, as well as an investigation into the persistence and dissipation. However, the specific parameter conditions for the coexistence of boundary equilibria and the bifurcation scenarios remain unexplored. Thus, we give the conditions for the coexistence of boundary equilibria where parameters lie in the 12-dimensional semi-algebraic space. Moreover, we investigate the local stability at the boundary equilibria and the global stability of the system. Furthermore, it is shown that the system exhibits saddle-node bifurcation and Hopf bifurcation. Numerical simulations are presented to illustrate that the three species in system can transition from unstable to a relatively stable coexistence state under antipredator effects.</p>

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Dynamics of a Tri-Trophic Predation Model with Antipredator Behavior and Beddington-DeAngelis Functional Response

  • 期刊论文

  • 发表日期：

    2025年6月23日

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  • Xiangxiang Jin,
  • Jie Li,
  • Lingling Liu

摘要

In this paper, we discuss a three-dimensional food web system that incorporates antipredator behavior. Previous studies have included the existence and local stability of the boundary equilibria, as well as an investigation into the persistence and dissipation. However, the specific parameter conditions for the coexistence of boundary equilibria and the bifurcation scenarios remain unexplored. Thus, we give the conditions for the coexistence of boundary equilibria where parameters lie in the 12-dimensional semi-algebraic space. Moreover, we investigate the local stability at the boundary equilibria and the global stability of the system. Furthermore, it is shown that the system exhibits saddle-node bifurcation and Hopf bifurcation. Numerical simulations are presented to illustrate that the three species in system can transition from unstable to a relatively stable coexistence state under antipredator effects.