Long-time behaviors of two stochastic mussel-algae models

Dengxia Zhou; Meng Liu; Ke Qi; Zhijun Liu; Dengxia Zhou; Meng Liu; Ke Qi; Zhijun Liu

doi:10.3934/mbe.2021416

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 6: 8392-8414. doi: 10.3934/mbe.2021416

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Research article

Long-time behaviors of two stochastic mussel-algae models

1.
School of Mathematics and Statistics, Hubei Minzu University, Enshi, Hubei 445000, China
2.
School of Mathematics and Statistics, Huaiyin Normal University, Huaian 223300, China

Academic Editor: Tonghua Zhang

Received: 25 July 2021 Accepted: 21 September 2021 Published: 27 September 2021

In this paper, we develop two stochastic mussel-algae models: one is autonomous and the other is periodic. For the autonomous model, we provide sufficient conditions for the extinction, nonpersistent in the mean and weak persistence, and demonstrate that the model possesses a unique ergodic stationary distribution by constructing some suitable Lyapunov functions. For the periodic model, we testify that it has a periodic solution. The theoretical findings are also applied to practice to dissect the effects of environmental perturbations on the growth of mussel.
- mussel-algae models,
- random perturbations,
- stationary distribution,
- periodic solution
Citation: Dengxia Zhou, Meng Liu, Ke Qi, Zhijun Liu. Long-time behaviors of two stochastic mussel-algae models[J]. Mathematical Biosciences and Engineering, 2021, 18(6): 8392-8414. doi: 10.3934/mbe.2021416

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Abstract

In this paper, we develop two stochastic mussel-algae models: one is autonomous and the other is periodic. For the autonomous model, we provide sufficient conditions for the extinction, nonpersistent in the mean and weak persistence, and demonstrate that the model possesses a unique ergodic stationary distribution by constructing some suitable Lyapunov functions. For the periodic model, we testify that it has a periodic solution. The theoretical findings are also applied to practice to dissect the effects of environmental perturbations on the growth of mussel.

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