A detailed examination of the effect of harvesting on a population has been carried out by extending the standard cubic deterministic model by considering a population under Allee effect with a quadratic function representing harvesting. Weak and strong Allee effect transitions, carrying capacity, and Allee threshold change according to harvesting are first discussed in the deterministic model. A Fokker–Planck equation has been obtained starting from a Langevin equation subject to correlated Gaussian white noise with zero mean, and an Approximate Fokker–Planck Equation has been obtained from a Langevin equation subject to correlated Gaussian colored noise with zero mean. This allowed to calculate the stationary probability distributions of populations, and thus to discuss the effects of linear and nonlinear (Holling type-II) harvesting for populations under Allee effect and subject to white and colored noises, respectively.

中文翻译：

---

具有收获的三次人口模型的确定性和随机性研究

通过考虑在 Allee 效应下的人口以及代表收获的二次函数，扩展标准三次确定性模型，对收获对人口的影响进行了详细检查。在确定性模型中首先讨论了根据收获的弱和强 Allee 效应转换、承载能力和 Allee 阈值变化。一个 Fokker-Planck 方程是从一个具有零均值的相关高斯白噪声的 Langevin 方程得到的，并且一个近似的 Fokker-Planck 方程是从一个具有零均值的相关高斯有色噪声的 Langevin 方程得到的。这允许计算人口的平稳概率分布，