@article{Kang2026, 
author = {Jin Kang and Rong Liu and Xuhui Shen},
title = {Dynamics of a stochastic single species model with mean-reverting Ornstein-Uhlenbeck and Allee effect},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {16264-16287},
keywords = {Ornstein-Uhlenbeck process, Allee effect, density function, stationary distribution, extinction},
url = {https://www.sciopen.com/article/10.3934/math.2026668},
doi = {10.3934/math.2026668},
abstract = {This paper studies the dynamics of a stochastic single species model with Ornstein-Uhlenbeck process and Allee effect. First, we establish the existence of a unique global solution and obtain moment estimates. Then, sufficient conditions for the existence of a unique stationary distribution of the model and for the extinction of species are derived. The results show that a weaker attack rate guarantees a unique stationary distribution, whereas a stronger attack rate leads to species extinction. Moreover, we obtain an approximate expression for the stationary density around the stochastic quasi-positive equilibrium by solving the associated Fokker-Planck equation. Finally, some numerical simulations are presented.}
}