Integrated pest management is a pest control strategy that combines biological and chemical methods to reduce environmental pollution and protect biodiversity. Recent research indicated that the fear caused by predators had a significant effect on the growth, development, and reproductive processes of prey. Therefore, we have proposed a pest-natrual enemy system, which is a nonlinear state-dependent feedback control model that incorporated the fear effect in the predator-prey relationship. We discussed impulsive sets and phase sets of the model and derived an expression for the Poincaré map. Furthermore, we analyzed the existence and stability of order-$ 1 $ periodic solutions and explored the existence of order-$ k $ $ (k\ge2) $ periodic solutions. Finally, numerical simulations were conducted to validate our theoretical results and reveal their biological implications.
Citation: Zhanhao Zhang, Yuan Tian. Dynamics of a nonlinear state-dependent feedback control ecological model with fear effect[J]. AIMS Mathematics, 2024, 9(9): 24271-24296. doi: 10.3934/math.20241181
Integrated pest management is a pest control strategy that combines biological and chemical methods to reduce environmental pollution and protect biodiversity. Recent research indicated that the fear caused by predators had a significant effect on the growth, development, and reproductive processes of prey. Therefore, we have proposed a pest-natrual enemy system, which is a nonlinear state-dependent feedback control model that incorporated the fear effect in the predator-prey relationship. We discussed impulsive sets and phase sets of the model and derived an expression for the Poincaré map. Furthermore, we analyzed the existence and stability of order-$ 1 $ periodic solutions and explored the existence of order-$ k $ $ (k\ge2) $ periodic solutions. Finally, numerical simulations were conducted to validate our theoretical results and reveal their biological implications.
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