具有隐藏状态的随机营养物质–浮游植物模型的长期行为
Long-Term Behavior of a Randomnutrient- Phytoplankton Model with Hidden State
摘要: 本文主要研究具有隐藏状态的营养物质–浮游植物模型的长期行为。首先，构造适当的李雅普诺夫函数，利用强马尔可夫性质，证明具有隐藏状态的随机营养物质–浮游植物模型解的存在唯一性和费勒过程；其次，讨论由非线性滤波器的遍历性和李雅普诺夫函数构造的阈值λ；最后，再运用弱收敛性和强大数定律等相关知识，证明了具有隐藏状态的随机营养物质–浮游植物模型解的灭绝性和持久性。
Abstract: This article mainly studies the long-term behavior of a nutrient-floating plant model with a hidden state. Firstly, the properly constructed Lee Yapanov function, using strong Marcov’s nature to prove that the existence of random nutrients with a hidden state-floating plant model solution is unique and Ferler’s process; secondly, discuss the ergodicity of nonlinear filters and the threshold con-structed by Lyapunov functions; finally, by applying relevant knowledge such as weak convergence and strong laws of large numbers, the extinction and persistence of solutions for the stochastic nu-trient phytoplankton model with hidden states were proved.
文章引用：杨争, 黄燕慧, 陈琳芳, 许文清, 黄在堂. 具有隐藏状态的随机营养物质–浮游植物模型的长期行为[J]. 应用数学进展, 2023, 12(11): 4884-4897. https://doi.org/10.12677/AAM.2023.1211481

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