The problem of equilibrium of non-linear dynamic system for microorganism in continuous culture is considered in this paper. The existence of equilibrium point is proved. The conclusion that the equilibrium is the con...The problem of equilibrium of non-linear dynamic system for microorganism in continuous culture is considered in this paper. The existence of equilibrium point is proved. The conclusion that the equilibrium is the continuous function of the dilution rate and substrate concentration in medium in a certain range is concluded. And the stability criterion of equilibrium is obtained. In theory, it explains the multiplicity shown in laboratory.展开更多
According to the recent investigation on cell cycle of fission yeast, a mathematical dynamic model is for-mulated. Four cyclins, e.g. Puc1, Cig1, Cig2 and Cdc13, are investigated here. The interacting networks between...According to the recent investigation on cell cycle of fission yeast, a mathematical dynamic model is for-mulated. Four cyclins, e.g. Puc1, Cig1, Cig2 and Cdc13, are investigated here. The interacting networks between the cy-clins and the process of cell cycle are mathematically de-scribed. The functions of these cyclins are particularly ana-lyzed. Comparison among different mutants indicates that the cyclins play an important role in cell cycle.展开更多
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
文摘The problem of equilibrium of non-linear dynamic system for microorganism in continuous culture is considered in this paper. The existence of equilibrium point is proved. The conclusion that the equilibrium is the continuous function of the dilution rate and substrate concentration in medium in a certain range is concluded. And the stability criterion of equilibrium is obtained. In theory, it explains the multiplicity shown in laboratory.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China(Grant No.20176005).
文摘According to the recent investigation on cell cycle of fission yeast, a mathematical dynamic model is for-mulated. Four cyclins, e.g. Puc1, Cig1, Cig2 and Cdc13, are investigated here. The interacting networks between the cy-clins and the process of cell cycle are mathematically de-scribed. The functions of these cyclins are particularly ana-lyzed. Comparison among different mutants indicates that the cyclins play an important role in cell cycle.
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.
