Study On The Stability Of A Variety Of Nonlinear Microbial Fermentation Dynamical Systems

With the increasing shortage of global energy and the rising of oil prices,the production of bio-based chemicals has gradually attracted people's attention.The microbial fermentation method of producing 1,3-propanediol is brought into sharp focus cause its merits of mild con-ditions,simple operations,fewer by-products,and green and environmental protections.On the research background of the actual processes of producing 1,3-propanediol,the stability and control theories of nonlinear dynamic systems and numerical calculation methods of ordinary differential equations are used to investigate the stability of non-linear dynamical systems cat-alyzed by multi-dimensional microbial fermentation enzymes.The work can not only enrich the stability theory of nonlinear dynamical systems,but also provide a reference for the industri-al production of 1,3-propanediol.Therefore,this research has some feature for the theoretical research and practical applications.The main results are summarized as follows:1.Considering the inhibitory effect of 3-hydroxypropionaldehyde on cell growth,the trans-port mode of glycerol and 1,3-propanediol across the cell membrane,and all possible metabolic pathways,the stability of a nonlinear non-differentiable dynamic system describing the microbial continuous fermentation process is discussed.Firstly,the existence of equilibrium point of the dynamic system is proved and the equilibrium point is obtained by numerical methods.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 Ja-cobian matrix and a third-order tensor are derived in the effective domain.The expression of the third-order tensor is presented.At last,an approximate linear system for the nonlinear dynamic system is constructed and its local stability is obtained.Thus,the nonlinear dynamic system is asymptotically stable.2.The strong stability of a nonlinear multistage dynamic system with no equilibrium point describing the microbial batch fermentation process is studied.For the batch fermentation pro-cess,the dynamic system is divided into three stages:development period,growth period,and stabilization period.Because the analytical solution of the dynamic system cannot be obtained,a homogeneous linear variation system for the solutions of the nonlinear system in different stages and the corresponding fundamental matrix solutions are constructed.The properties of the fun-damental matrix solution and the strong stability of the nonlinear multistage dynamical system are derived.3.The strong stability of a nonlinear time-delay dynamical system catalyzed by a micro-bial batch-fermentation enzyme is discussed.First,since the system has no equilibrium point and the analytical solution cannot be obtained,a nonhomogeneous linear variation time-delay system for the solutions of the nonlinear time-delay system and the corresponding fundamental matrix solutions are constructed.Then,based on the nonhomogeneous and time-delay proper-ties of the linear variational systems,the properties of the fundamental matrix solutions in every sub-domain are discussed and the boundedness of the fundamental matrix solution are proved.Finally,the strong stability of the nonlinear dynamic system with time delay is obained.