<p>This paper proposes and analyzes a new mathematical model for a three-species food chain and incorporates the structure stage in the middle predator. The model considers various factors such as fear, anti-predator behavior of prey, and interspecific competition. The prey-predator interaction is modeled using a Holling type II functional response. Our analysis has demonstrated that the model system is both positive and bounded, and we have also determined the local stability condition for each equilibrium point. The Hopf bifurcation analysis results have revealed that the model system’s stability is affected by important parameters. Finally, we have provided numerical simulations to demonstrate our theoretical findings. Simulation results show that a low counterattack rate and medium level of fear of prey are beneficial for maintaining the stability of the coexistence equilibrium point. A low juvenile growth rate for the middle predator can prevent the population from surviving and developing in both the juvenile and adult stages.</p>

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Dynamical analysis of a stage-structured food-chain model under fear effect and anti-predator behavior

  • Thuy Phuong Nguyen,
  • Thao Dieu Do,
  • Huyen Thi-Thu Nguyen

摘要

This paper proposes and analyzes a new mathematical model for a three-species food chain and incorporates the structure stage in the middle predator. The model considers various factors such as fear, anti-predator behavior of prey, and interspecific competition. The prey-predator interaction is modeled using a Holling type II functional response. Our analysis has demonstrated that the model system is both positive and bounded, and we have also determined the local stability condition for each equilibrium point. The Hopf bifurcation analysis results have revealed that the model system’s stability is affected by important parameters. Finally, we have provided numerical simulations to demonstrate our theoretical findings. Simulation results show that a low counterattack rate and medium level of fear of prey are beneficial for maintaining the stability of the coexistence equilibrium point. A low juvenile growth rate for the middle predator can prevent the population from surviving and developing in both the juvenile and adult stages.