@article{Zhang2024, 
author = {Zhanhao Zhang and Yuan Tian},
title = {Dynamics of a nonlinear state-dependent feedback control ecological model with fear effect},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {9},
pages = {24271-24296},
keywords = {integrated pest management, Poincaré map, periodic solution, existence and stability, fear effect},
url = {https://www.sciopen.com/article/10.3934/math.20241181},
doi = {10.3934/math.20241181},
abstract = {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≥2) periodic solutions. Finally, numerical simulations were conducted to validate our theoretical results and reveal their biological implications.}
}