Premium
Stationary distribution and extinction for a food chain chemostat model with random perturbation
Author(s) -
Gao Miaomiao,
Jiang Daqing,
Hayat Tasawar,
Alsaedi Ahmed
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6809
Subject(s) - chemostat , stationary distribution , mathematics , food chain , ergodic theory , extinction (optical mineralogy) , uniqueness , lyapunov function , perturbation (astronomy) , predation , white noise , statistical physics , environmental noise , ecology , mathematical analysis , statistics , markov chain , biology , nonlinear system , physics , paleontology , genetics , quantum mechanics , bacteria , acoustics , sound (geography)
In this paper, we study the dynamical behavior of a stochastic food chain chemostat model, in which the white noise is proportional to the variables. Firstly, we prove the existence and uniqueness of the global positive solution. Then by constructing suitable Lyapunov functions, we show the system has a unique ergodic stationary distribution. Furthermore, the extinction of microorganisms is discussed in two cases. In one case, both the prey and the predator species are extinct, and in the other case, the prey species is surviving and the predator species is extinct. Finally, numerical experiments are performed for supporting the theoretical results.