This paper investigates the stochastic dynamics of trophic cascade chemostat model perturbed by regime switching, Gaussian white noise and impulsive toxicant input. For the system with only white noise interference, s...This paper investigates the stochastic dynamics of trophic cascade chemostat model perturbed by regime switching, Gaussian white noise and impulsive toxicant input. For the system with only white noise interference, sufficient conditions for stochastically ultimate boundedness and stochastically permanence are obtained, and we demonstrate that the stochastic system has at least one nontrivial positive periodic solution. For the system with Markov regime switching, sufficient conditions for extinction of the microorganisms are established. Then we prove the system is ergodic and has a stationary distribution. The results show that both impulsive toxins input and stochastic noise have great effects on the survival and extinction of the microorganisms. Finally, a series of numerical simulations are presented to illustrate the theoretical analysis.展开更多
基金the National Natural Science Foundation of China (No.12271308)the Research Fund for the Taishan Scholar Project of Shandong Province of ChinaShandong Provincial Natural Science Foundation of China (ZR2019MA003)。
文摘This paper investigates the stochastic dynamics of trophic cascade chemostat model perturbed by regime switching, Gaussian white noise and impulsive toxicant input. For the system with only white noise interference, sufficient conditions for stochastically ultimate boundedness and stochastically permanence are obtained, and we demonstrate that the stochastic system has at least one nontrivial positive periodic solution. For the system with Markov regime switching, sufficient conditions for extinction of the microorganisms are established. Then we prove the system is ergodic and has a stationary distribution. The results show that both impulsive toxins input and stochastic noise have great effects on the survival and extinction of the microorganisms. Finally, a series of numerical simulations are presented to illustrate the theoretical analysis.
