We study a stochastic population growth model with Allee effect, it is driven by correlated multiplicative and additive colored noises. The influences of noises on the statistical properties of the stochastic model are discussed. Applying an approximative Fokker-Planck equation, we first obtain the stationary probability distribution (SPD) of the stochastic model, and then present a more detailed discussion of how the noises determine the behaviors of the SPD, mean, variance and skewness of the population size. The research of the shape of SPD shows that the phenomenological bifurcation may occur when the noise intensity passes through a critical value. We also find that the additive and multiplicative noises have different effects on the moments (mean, variance and skewness) of population density.

中文翻译：

---

有色噪声对具有 Allee 效应的人口增长模型统计特性的影响

我们研究了具有 Allee 效应的随机人口增长模型，它由相关的乘法和加法有色噪声驱动。讨论了噪声对随机模型统计特性的影响。应用近似的 Fokker-Planck 方程，我们首先获得随机模型的平稳概率分布 (SPD)，然后更详细地讨论噪声如何决定 SPD 的行为、总体规模的均值、方差和偏度. SPD形状的研究表明，当噪声强度超过临界值时，可能会出现现象学分叉。我们还发现加性和乘性噪声对人口密度的矩（均值、方差和偏度）有不同的影响。