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| 具有Allee效应的加性随机捕食模型的动力学研究 |
| Dynamics Analysis of an Additive Stochastic Predator-Prey Model with Allee Effect |
| 投稿时间：2023-08-29 修订日期：2024-01-13 |
| DOI： |
| 中文关键词: 随机捕食食饵模型 Allee效应 灭绝性 遍历性 |
| 英文关键词: Stochastic Predator-Prey Model Allee Effect Extinction Ergodicity |
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| 中文摘要: |
| 生态系统中捕食者和被捕食者受到群聚生活的影响，Allee效应充分反映种群大小、密度及其增长率之间的相互作用。同时，生态系统会受到随机因素的影响。因此，本文研究具有Allee效应的加性随机捕食模型的动力学行为。首先利用不动点原理研究模型解的存在唯一性。然后构造恰当 函数证明模型解的遍历性和灭绝性。最后，给出相关数值仿真验证结果的可靠性 |
| 英文摘要: |
| Predators and prey in ecosystems are affected by social life, and the Allee effect fully reflects the interaction between population size, density, and growth rate. In addition, ecosystems are subject to random factors. Therefore, the dynamic behavior of additive stochastic prey-predator model with Allee effect are studied in this paper. By constructing a suitable stochastic Lyapunov function, we obtain sufficient conditions for extinction of the predator species and establish sufficient conditions for the existence of an ergodic stationary distribution of the positive solution to such system. In addition, some numerical simulation results are given. |
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