The present study takes advantage of the white noise and the Lévy noise to portray the small and sudden environmental perturbations respectively, and puts forward a stochastic population model with Allee effects and Lévy jumps. First, it is confirmed that the model possesses a unique, global and positive solution. Then, permanence and extinction of the species are examined. Afterwards, the trajectory of population abundance is tested. The findings uncover that both the white noise and the Lévy noise have significant functions on the rate of population change. Finally, the theoretical findings are applied to dissect the rate of population change of the African hunting dog Lycaon pictus.

中文翻译：

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关于具有Allee效应和环境扰动的人口模型

本研究利用白噪声和Lévy噪声分别刻画了环境的小扰动和突发性环境扰动，并提出了具有Allee效应和Lévy跳变的随机种群模型。首先，可以确定该模型具有唯一，全局和正解。然后，检查物种的持久性和灭绝性。然后，测试人口数量的轨迹。研究结果发现，白噪声和列维噪声均对人口变化率具有重要作用。最后，将理论发现应用于剖析非洲猎犬Lycaon pictus的种群变化率。