Abstract
In this paper, we present a stochastic eutrophication-chemostat model with impulsive dredging and pulse inputting on environmental toxicant. The sufficient condition for the extinction of microorganisms is obtained. The sufficient condition for the investigated system with unique ergodic stationary distribution is also obtained. The results show that the stochastic noise, impulsive dredging, and pulse input on the environmental toxicant play important roles in the extinction of microorganisms. The results also indicate the effective and reliable controlling strategy for water resource management. Finally, numerical simulations are employed to illustrate our results.
Highlights
The chemostat is a device for continuous and impulsive cultures of microorganisms in laboratory [1,2,3]
2 The model Inspired by the above discussion, we consider a stochastic eutrophication-chemostat model with impulsive dredging and pulse inputting on environmental toxicant:
6 Discussion In this work, we consider a stochastic eutrophication-chemostat model with impulsive dredging and pulse inputting on environmental toxicant
Summary
The chemostat is a device for continuous and impulsive cultures of microorganisms in laboratory [1,2,3]. Where x(t) is the concentration of the nutrient in a lake at time t. Y(t) is the concentration of the microorganism in a lake at time t. Co(t) is the concentration of the toxicant in the organism of the microorganism in a lake at time t. Ce(t) is the concentration of the toxicant in a lake at time t. F > 0 is the coefficient of the population organism’s net uptake of toxicant from the environment in a lake. 0 < h1 < 1 is the effect of impulsive dredging microorganism at time t = (n+l) (0 < l < 1). 0 < h2 < 1 is the effect of impulsive dredging environmental toxicant at time t = (n + l) (0 < l < 1).
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