This paper investigates a stochastic Holling II predator-prey model with Lévy jumps and habit complexity. It is first proved that the established model admits a unique global positive solution by employing the Lyapunov technique, and the stochastic ultimate boundedness of this positive solution is also obtained. Sufficient conditions are established for the extinction and persistence of this solution. Moreover, some numerical simulations are carried out to support the obtained results.

中文翻译：

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具有 Lévy 跳跃和栖息地复杂性的随机 Holling II 捕食者 - 猎物模型的动力学

本文研究了具有 Lévy 跳跃和习惯复杂性的随机 Holling II 捕食者 - 猎物模型。首先利用Lyapunov技术证明了所建立的模型具有唯一的全局正解，并得到了该正解的随机最终有界性。为这种解决方案的消失和持久性建立了充分的条件。此外，还进行了一些数值模拟来支持所获得的结果。