Dynamical Analysis of Nonautonomous Trophic Cascade Chemostat Model with Regime Switching and Nonlinear Perturbations in a Polluted Environment  

作　　者：Ya-jie LI Hao-kun QI Zheng-bo CHANG Xin-zhu MENG 

机构地区：[1]College of Mathematics and Systems Science,Shandong University of Science and Technology,Qingdao 266590,China [2]Weifang Commercial College of Shandong,Weifang 261011,China [3]College of Mathematics and Information Science,Anshan Normal University,Anshan 114007,China

出　　处：《Acta Mathematicae Applicatae Sinica》2023年第3期550-570,共21页应用数学学报（英文版）

基　　金：the National Natural Science Foundation of China (No.12271308);the Research Fund for the Taishan Scholar Project of Shandong Province of China;Shandong Provincial Natural Science Foundation of China (ZR2019MA003)。

摘　　要：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.

关 键 词：stochastic trophic cascade chemostat model Markov chain extinction and stochastic permanence periodic solution ERGODICITY 

分 类 号：X502[环境科学与工程—环境工程]