This paper considers the fed-batch culture in microbial fermentation process, which consists of batch and continuous culture. The goal is to explore the properties of a novel model which can describe the characteristi...This paper considers the fed-batch culture in microbial fermentation process, which consists of batch and continuous culture. The goal is to explore the properties of a novel model which can describe the characteristics of multistage for the population growth of microorganisms in nonlinear switch dynamic system. The improved model is developed based on the experimental data to describe the delayed, developmental and stationary stages well for the phases of batch culture. Then the existence, uniqueness and boundedness of solutions to the nonlinear multistage switch system and the Lipschitz continuity and differentiability of solutions with respect to the initial state is discussed as well. Finally, a numerical simulation is employed for the nonlinear multistage switch system.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11171050,11101262 and 11371164the National Natural Science Foundation for the Youth of China under Grant Nos.11301081,11401073
文摘This paper considers the fed-batch culture in microbial fermentation process, which consists of batch and continuous culture. The goal is to explore the properties of a novel model which can describe the characteristics of multistage for the population growth of microorganisms in nonlinear switch dynamic system. The improved model is developed based on the experimental data to describe the delayed, developmental and stationary stages well for the phases of batch culture. Then the existence, uniqueness and boundedness of solutions to the nonlinear multistage switch system and the Lipschitz continuity and differentiability of solutions with respect to the initial state is discussed as well. Finally, a numerical simulation is employed for the nonlinear multistage switch system.
