Dynamics of a nonlinear state-dependent feedback control ecological model with fear effect

Author:

Zhang Zhanhao1,Tian Yuan12

Affiliation:

1. School of Mathematics and Statistics, Hubei Minzu University, Enshi, 445000, China

2. Hubei Key Laboratory of Biologic Resources Protection and Utilization, Hubei Minzu University, Enshi, 445000, China

Abstract

<p>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.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

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