Due to many uncertain factors,parameter values in many microorganism cultivation systems are affected to a greater or lesser extent by environmental fluctuation.In this paper,the authors develop a stochastic turbidost...Due to many uncertain factors,parameter values in many microorganism cultivation systems are affected to a greater or lesser extent by environmental fluctuation.In this paper,the authors develop a stochastic turbidostat model that considers white noise,formulate and analyze dynamical behavior for the stochastic model.The authors obtain the existence and uniqueness of globally positive equilibrium.Sufficient conditions of the extinction for the system are established.Since the uniformly elliptic condition can fail to satisfy,the existence of the stationary distribution of the system is proved by using Markov semigroups theory.Biologically speaking,the existence of stationary distribution suggests that microorganism will exist for a long time.The analytical results are tested and verified by numerical simulations,which evaluate the influence of white noise on the dynamics of microorganism.展开更多
基金This research was supported by the Natural Science Foundation of China under Grant Nos.11871473 and 12271201the Research Funds for Department of Science and Technology of Jilin Province under Grant No.20210509040RQ+2 种基金Innovation and Entrepreneurship Talent Funds of Jilin Province under Grant No.2022ZY22the Research Funds of Jilin University of Finance and Economics under Grant No.2022YB025Shandong Provincial Natural Science Foundation under Grant Nos.ZR2019MA010 and ZR2019MA006.
文摘Due to many uncertain factors,parameter values in many microorganism cultivation systems are affected to a greater or lesser extent by environmental fluctuation.In this paper,the authors develop a stochastic turbidostat model that considers white noise,formulate and analyze dynamical behavior for the stochastic model.The authors obtain the existence and uniqueness of globally positive equilibrium.Sufficient conditions of the extinction for the system are established.Since the uniformly elliptic condition can fail to satisfy,the existence of the stationary distribution of the system is proved by using Markov semigroups theory.Biologically speaking,the existence of stationary distribution suggests that microorganism will exist for a long time.The analytical results are tested and verified by numerical simulations,which evaluate the influence of white noise on the dynamics of microorganism.
基金Acknowledgments The authors would like to thank the editors and the anonymous referees for their helpful suggestions and comments which led to the improvement of our original manuscript. This work is supported by the National Natural Science Foundation of China （Grant Nos. 11561022, 11261017）, the China Postdoctoral Science Foundation （Grant No. 2014M562008）.
基金supported by the the National Natural Science Foundation of China(No.11371164)NSFC-Talent Training Fund of Henan(U1304104)Henan Science and Technology Department(122300410398,132300410084)
