Dynamical behavior of a stochastic food chain chemostat model with variable yields. (English) Zbl 1519.92131
Summary: In this paper, we consider a stochastic food chain chemostat model with variable yields. First, we prove the stochastic model has a unique global positive solution. Second, by employing suitable Lyapunov functions, Itô’s formula and some other important inequalities, the existence of a unique ergodic stationary distribution of a stochastic food chain chemostat model is researched, which can help us better understand the statistical characteristics of stochastic food chain chemostat models. Second, we investigate the extinction of the microorganism and the bacteria. Moreover, the case of extinction for bacteria but persistence for microbial species is considered. Finally, some numerical simulations are carried out to illustrate our theoretical results and the influence of the variable yields on the microorganism and the bacteria.
MSC:
| 92C75 | Biotechnology |
| 92D40 | Ecology |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 60G10 | Stationary stochastic processes |
Keywords:
stochastic food chain chemostat model; stochastic Lyapunov function; Itô’s formula; stationary distribution; extinction; variable yieldReferences:
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