Extinction and stationary distribution of an impulsive stochastic chemostat model with nonlinear perturbation

Dynamical Analysis of a Stochastic Multispecies Turbidostat Model

“…Subsequently, many researchers investigated turbidostat and chemostat systems. Many valuable and interesting results were obtained [11][12][13][14][15][16].…”

“…Xu et al [7] investigated a chemostat model containing telegraph noise with the help of Markov chain and derived the break-even concentration which determines the persistence or extinction 2 Complexity of microorganisms. One can also find a large number of stochastic models on cultivation of microorganisms [14,15,[20][21][22][23] as well as in other fields [24][25][26][27][28].…”

Dynamics of a stochastic eutrophication-chemostat model with impulsive dredging and pulse inputting on environmental toxicant

“…Specially, the toxicant and abundant microorganisms in the water pollution environment are also a threat to the water resource management. Consequently, it is important to discuss chemostat models in a polluted environment [6,7]. Zhou et al [8] considered that reservoir dredging is the main and effective way to improve water quality by using a physical method.…”

“…Mao [9,10] investigated stochastic differential equations and their applications. Lv et al [11] presented an impulsive stochastic chemostat model with nonlinear perturbation.…”

Dynamical Analysis of a Stochastic Predator-Prey System with Lévy Noise and Impulsive Toxicant Input

“…They obtained a set of sufficient conditions for extinction, weak persistence in the mean and global attraction to any positive solution of the system. Lv, Meng and Wang [12] investigated an impulsive stochastic chemostat model with nonlinear perturbation in a polluted environment. They showed that both stochastic and impulsive toxicant inputs have great effects on the survival and extinction of the microorganism.…”