Mathematical Biosciences and Engineering (Sep 2021)

Long-time behaviors of two stochastic mussel-algae models

  • Dengxia Zhou,
  • Meng Liu,
  • Ke Qi,
  • Zhijun Liu

DOI
https://doi.org/10.3934/mbe.2021416
Journal volume & issue
Vol. 18, no. 6
pp. 8392 – 8414

Abstract

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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.

Keywords