The Parameter's Effect on the Stability in Microbial Growth Model

Abstract

A nonlinear dynamic growth model of microorganisms is developed by considering the chemotaxis, the diffusion, and the pH value based on the theories of the diffusion reaction of thermodynamics and the chemotactic reaction of biology in this paper. The stability of the model is studied by analyzing the growth rate and the frequency of the solutions of a small perturbation. When different parameter values are set, the effect of every parameter on the stability of the system is analyzed in detail. With a number of data analysis, the conclusion that the stability is mainly affected by two parameters, namely, the initial density of bacteria and the consumption rate of foods by bacteria when they are given the large enough values.