Novel model in kinetics of microbial batch culture

Logistic equation which is well known in the field of ecology is introduced into the study of the kinetics of microbial batch culture. Three models of microbial concentration (x) in the culture medium as functions of substrate concentration (s) respectively based on Monod equation, Herbert equation and Logistic equation are established for comparison. And these models are simulated according to experimental data to testify their validity. It is valuable in the study of microbial culture to introduce a significant model in macrosmatic domain into microcosmic microbial experiments and theoretical study as a precise microbial kinetic equation, and this will help to further the study of the oxidative decomposition process of degradable organic substances decomposed by microorganism in water environment, which will lead to novel biological water quality models in river, lake, reservoir and etc.. The numerical methods used in this study are nonlinear Least-square and Interior-reflective Newton Method. The simulation coefficients in the models of x-s based on Logistic equation are 0.9940, 0.9867 respectively according to Lorynebacterium glutamicum batch culture and Pseudomonas sp. batch culture.