Asfaw Manalebish Debalike, Kassa Semu Mitiku, Lungu Edward M
Department of Mathematics, Addis Ababa University, Addis Ababa, Ethiopia.
Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology (BIUST), P/Bag 16, Palapye, Botswana.
J Math Biol. 2019 Dec;79(6-7):2183-2209. doi: 10.1007/s00285-019-01425-5. Epub 2019 Sep 5.
Environmental noises often affect population dynamics, and hence many benefits are gained in using stochastic models since real life is full of stochasticity and randomness. In this paper a stochastic extension of a model by Asfaw et al. (Int J Biomath 11:1850057, 2018) is considered. Due to the non-linearity of the model, first, a simplified stochastic plant-herbivore model is formulated and analyzed for its global Lipschitz continuity, positivity, existence and uniqueness of solutions. Second, the analysis is extended to a more complex and realistic model. Numerical simulations using Euler-Maruyama method are employed to demonstrate the long term dynamics. It was found that the noise added to the herbivore population resulted more change in the dynamics than the noise added to the plant population (food source). Ignoring the environmental noise could make the land management and wild life conservation not to maintain their goals.
环境噪声常常影响种群动态，因此使用随机模型有诸多益处，因为现实生活充满了随机性和不确定性。本文考虑了阿斯法等人（《国际生物数学杂志》11:1850057，2018年）模型的随机扩展。由于该模型的非线性，首先，构建并分析了一个简化的随机植物 - 食草动物模型，以研究其全局李普希茨连续性、正性、解的存在性和唯一性。其次，将分析扩展到一个更复杂且更现实的模型。采用欧拉 - 丸山方法进行数值模拟，以展示长期动态。结果发现，添加到食草动物种群的噪声比添加到植物种群（食物来源）的噪声在动态变化上导致的变化更大。忽略环境噪声可能致使土地管理和野生动物保护无法实现其目标。
