Open AccessLong-time behaviors of two stochastic mussel-algae models
Author(s) -
Dengxia Zhou,
Meng Li,
Ke Qi,
Zhijun Liu
Publication year - 2021
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2021416
Subject(s) - ergodic theory , mussel , extinction (optical mineralogy) , lyapunov function , ecology , persistence (discontinuity) , stochastic modelling , mathematics , environmental science , statistical physics , biology , physics , mathematical analysis , geology , statistics , geotechnical engineering , paleontology , nonlinear system , quantum mechanics
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.