This paper investigates the dynamics of the stochastic predator–prey model with a Crowley–Martin functional response function driven by Lévy noise. First, the existence, uniqueness and boundedness of a global positive solution is proven. Next, the persfor an optimal conditions. Finally, the theoretical results are reinforced by some numerical simulations. We illustrated the sufficient conditions to classify the dynamics of the stochastic predator–prey model.

中文翻译：

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具有Crowley-Martin功能反应和阶段结构的随机捕食者-食饵Lévy跳跃模型

本文研究了由Lévy噪声驱动的具有Crowley-Martin功能响应函数的随机捕食者-被捕食模型的动力学。首先，证明了全球肯定解决方案的存在，唯一性和有界性。接下来，选择最佳条件。最后，通过一些数值模拟加强了理论结果。我们举例说明了分类随机捕食者－猎物模型动力学的充分条件。