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Microbial growth is a very complex non-linear system, so there is important engineering significance to study its growth model in holding back biofouling, eliminating biofouling and preventing corrosion. In this paper, a non-linear dynamic model of microbial growth was built based on the theories of the diffusion response of thermodynamics and the chemotactic response of biology. The model involves three variables, the density of bacteria, the concentration of attractant and the pH value. A temporal linear instability is carried out to analyze the stability of the model. The relationship between the growth rate 6 and the wavenumber kappa is expressed by a cubic equation. The results reveal that the stability of three variables does not exist under the conditions involved in present paper.