Study On The Stability And Nonlinear Characteristics Of Microbial Growth

The nonlinear partial differential equations of microbial growth and the nonlinear evolution differential equations of microbial population are developed based on the theories of the diffusion response of thermodynamics, the chemotactic response of biology and the effect of pH on microbial growth in this thesis. The stability is analyzed by using time small perturbation method and linearization method of nonlinear equations, and a series of innovative results are obtained. This is significant to understand the growth and evolution of microorganisms and the corresponding theories. The major work and research results in this thesis are as follows:First, the nonlinear partial differential equations of microbial growth and the nonlinear evolution differential equations of microbial population are developed.Second, some parameters such as q ,μ,κ,η, s and u 0 which affect the stability of the system are studied respectively by using small perturbation method in the phase space and some valuable conclusions are drawn.Then, three different models are developed by ignoring the effect of the pH value, ignoring the effect of chemotaxis and considering the effects of both the two factors. Then the effects of pH and the reproduction rate of bacteria on the stability of the system are studied.Finally, the governing equations of microbial population in a certain isolated spatial domain are deduced and the global asymptotical behavior of solutions is studied by making nonlinear equations linearization method, namely Lyapunov indirect method. For the tree-variable model, the Routh-Hurwitz theorem is adopted to determine the asymptotical behavior.Finally, numerical methods such as the three-step time-advancement method (third-order TVD Runge-Kutta scheme) and the second-order central differences for the spatial derivatives are adopted to solve the governing equations and the evolution of stimulations on the whole system is carried out.