Open AccessA stochastic mussel-algae model under regime switching
Author(s) -
Yan Xie,
Zhijun Liu,
Ke Qi,
Dongchen Shangguan,
Qinglong Wang
Publication year - 2022
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.2022224
Subject(s) - mussel , ergodic theory , stochastic differential equation , extinction (optical mineralogy) , lyapunov function , stochastic modelling , stochastic process , stationary distribution , mathematics , statistical physics , computer science , ecology , physics , biology , nonlinear system , mathematical analysis , statistics , markov chain , quantum mechanics , optics
We investigate a novel model of coupled stochastic differential equations modeling the interaction of mussel and algae in a random environment, in which combined effect of white noises and telegraph noises formulated under regime switching are incorporated. We derive sufficient condition of extinction for mussel species. Then with the help of stochastic Lyapunov functions, a well-grounded understanding of the existence of ergodic stationary distribution is obtained. Meticulous numerical examples are also employed to visualize our theoretical results in detail. Our analytical results indicate that dynamic behaviors of the stochastic mussel-algae model are intimately associated with two kinds of random perturbations.