Stability Of Multiform Dynamical Systems In Microbial Fermentation

With the rapid development of "Green economy",based on the needs of eco-friendly,production safety and sustainable development,the method of microbial fermentation to produce 1,3-propanediol has replaced the chemical industry manufacturing methods.In this dissertation,we study the strong stability and asymptotic stability of the nonlinear dynamic system in the process of microbial fermentation.The main contributions are summarized as follows.1.Considering that the substrate needs to be fully mixed for a certain period of time before the disproportionation reaction in batch fermentation,a nonlinear time-delay dynamical system without analytical solution and equilibrium point is studied.First,a nonhomogeneous linear variation time-delay system for the solutions of the nonlinear time-delay dynamical system is constructed,as well as the corresponding fundamental matrix.Then,based on the boundedness of the fundamental matrix solutions,the strong stability of the initial state vector disturbance of the nonlinear time-delay dynamical system is obtained.Finally,the numerical results verify the strong stability.2.For the batch fermentation process of a group of microorganisms,because the system state variables and their rate of change are smooth,in order to avoid the study of infinite dimension of continuous function space,the finite piecewise linear continuous function approach to any continuous function is adopted,and the optimization of infinite dimension is transformed into the optimization of finite dimension.In the nonlinear dynamic system of enzyme catalyzed batch fermentation,the piecewise continuous function is taken as the optimization parameter,and the system is divided into several subsystems.Through the linear variational system and the basic matrix solution,the strong stability of the solution of the dynamic system with respect to the initial value disturbance is studied.3.Considering the inhibitory effect of 3-hydroxypropionaldehyde on cell growth,the transport mode of glycerol and 1,3-propanediol across the cell membrane,and the most metabolic pathway,the stability of a nonlinear enzyme catalysis and gene regulation dynamic system in continuous fermentation is discussed.Firstly,the existence of the equilibrium point of the system is proved and the equilibrium point is obtained by numerical method.Then,in order to overcome the difficulty on the non-differentiability of the system,a differentiable effective domain is constructed near the equilibrium point,and local bounded properties of a Jacobian matrix and Hessian matrix are derived in the effective domain.At last,an approximate linear system for the nonlinear dynamical system is constructed and its local stability is proved by obtained.Thus,the nonlinear dynamical system is asymptotic stable.