Long-time behaviors of two stochastic mussel-algae models
Dengxia Zhou1, Meng Liu2, Ke Qi1
1School of Mathematics and Statistics, Hubei Minzu University, Enshi, Hubei 445000, China.
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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