The stationary distribution and ergodicity of a stochastic phytoplankton allelopathy model under regime switching

被引：72
作者：
Zhao, Yu [1 ,3 ]
Yuan, Sanling [2 ]
Zhang, Tonghua [4 ]
机构：
[1] Univ Shanghai Sci & Technol, Sch Business, Shanghai 200093, Peoples R China
[2] Univ Shanghai Sci & Technol, Coll Sci, Shanghai 200093, Peoples R China
[3] Ningxia Normal Univ, Sch Math & Comp Sci, Ningxia 756000, Guyuan, Peoples R China
[4] Swinburne Univ Technol, Dept Math, Hawthorn, Vic 3122, Australia
来源：
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2016年 / 37卷
基金：
中国国家自然科学基金;
关键词：
Ecotoxicology; Phytoplankton allelopathy; Stochastic disturbance; Markov chain; Stationary distribution; Ergodicity; DIFFERENTIAL-EQUATIONS; DYNAMICAL BEHAVIOR; PERSISTENCE; EXTINCTION; BLOOMS; SYSTEM;
D O I：
10.1016/j.cnsns.2016.01.013
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The effect of toxin-producing phytoplankton and environmental stochasticity are interesting problems in marine plankton ecology. In this paper, we develop and analyze a stochastic phytoplankton allelopathy model, which takes both white and colored noises into account. We first prove the existence of the global positive solution of the model. And then by using the stochastic Lyapunov functions, we investigate the positive recurrence and ergodic property of the model, which implies the existence of a stationary distribution of the solution. Moreover, we obtain the mean and variance of the stationary distribution. Our results show that both the two kinds of environmental noises and toxic substances have great impacts on the evolution of the phytoplankton populations. Finally, numerical simulations are carried out to illustrate our theoretical results. (C) 2016 Elsevier B.V. All rights reserved.
引用
收藏
页码：131 / 142
页数：12
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