随机扩散贻贝-藻类模型的动力学行为  

Long-term Behavior of a Stochastic Diffusive Mussel-Algae Model

作　　者：吕超 黄露秋 潘玉婷 黄在堂 LV Chao;HUANG Lu-qiu;PAN Yu-ting;HUANG Zai-tang(School of Mathematics and Statistics,Nanning Normal University,Nanning 530023,China)

机构地区：[1]南宁师范大学数学与统计学院,广西南宁530023

出　　处：《数学的实践与认识》2020年第22期244-257,共14页Mathematics in Practice and Theory

基　　金：国家自然科学基金(41665006,11561009);广西自然科学基金(2018GXNSFAA380240)。

摘　　要：主要研究随机扩散贻贝-藻类模型的长期性行为.首先,在噪声相互作用强度充分小时,构造适当的李雅普诺夫函数,证明了随机扩散贻贝-藻类模型存在唯一的全局正解.其次,在适当的条件下,利用比较定理,给出了随机扩散贻贝-藻类模型在均方意义上具有灭绝性和稳定性.最后,证明了随机扩散贻贝-藻类模型解的马尔可夫性和存在唯一的不变测度.This article focuses on the long-term behavior of the stochastic diffusive Mussel-Algae model.First,constructing a reasonable Lyapunov function,it is proved that the stochastic diffusive Mussel-Algae model has a sufficiently positive global solution when the interaction intensity is sufficiently small.Second,under certain additional conditions,by using the comparison theorem,the stochastic diffusive Mussel-Algae model proved to be extinct and stable in the mean square.Finally,the Markov property of the solution of the stochastic diffusive Mussel-Algae model was proved,and the unique invariant measure of the stochastic diffusive Mussel-Algae model was fully proved.

关 键 词：随机贻贝-藻类模型 全局解 存在性 马尔可夫性 不变测度 

分 类 号：O175[理学—数学]