随机浮游生物扩散模型的灭绝和平稳分布
Extinction and Stationary Distribution of Stochastic PlanktonDispersal Models
摘要: 本文研究了随机浮游生物扩散模型的渐近行为。 首先，构造合理的李雅普诺夫函数，证明了随机 浮游生物扩散模型正解的存在唯一性。 其次，利用比较定理，证明随机浮游生物扩散模型的灭绝 和均方稳定。 最后，运用扩散理论，证明了随机浮游生物扩散模型存在唯一平稳分布。
Abstract: In this paper, the asymptotic behavior of the stochastic plankton dispersal model is studied. Firstly, a reasonable Lyapunov function is constructed to prove the unique- ness of the positive solution of the stochastic plankton diffusion model. Secondly, the comparison theorem is used to prove the extinction and mean square stability of the random plankton dispersal model. Finally, the diffusion theory is used to prove that there is a unique stationary distribution of the stochastic plankton dispersal model.
文章引用：巫东兰, 黄梓轩, 钟志业, 陆玉梅. 随机浮游生物扩散模型的灭绝和平稳分布[J]. 应用数学进展, 2025, 14(5): 670-688. https://doi.org/10.12677/AAM.2025.145292

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