Dynamical Behavior Of Recombinant DNA Cell Culturing In Chemostat Models With Delayed Feedback Control

In order to enhance the artificial controllability and the efficiency in the process ofcontinuous microorganism culture, we often need to adjust and control the environmentof culture. But in the process of culture, there may have some indefinite factors (forexample, the existence of time lag) which may have some inevitable influence on thedynamic behaviors of system. In this paper, we investigate the dynamical behaviors oftwo chemostat-type models: one is the turbidostat models with delayed feedback controland the other is a chemostat model with a single microorganism competing onesubstrate with two delays. The outline of this paper is as follows:In the first chapter, we give a brief summary of researching background andsignificance of recombinant DNA cell culturing and introduce some newly developmentin this filed. At the end, we state the main results obtained in this paper.In the second chapter, the turbidostat model of single microorganism with delayedoutput feedback control is considered, where the delay models the time needed in themeasurement of the sensor to the turbidity of the nutrient of the fluid. Considering it asa bifurcation parameter, the conditions of the local stability of positive equilibrium andthe existence of Hopf bifurcation are obtained. Moreover, by using the normal formtheory and the center manifold theorem, the formula of the direction and stability of thebifurcating period solutions are determined. At last, computer simulations illustrate theresults.In the third chapter, a model of competition between the plasmid-bearing and theplasmid-free in a turbidostat with delayed feedback control is investigated. By choosingthe delay in the measurement of the sensor to the turbidity of the fluid as a parameter,we obtain the conditions of local stability of positive equilibrium and the existence ofHopf bifurcations. Moreover, by using the normal form theory and the center manifoldtheorem, the formula of the direction and stability of the bifurcating periodic solutionsare determined. Computer simulations illustrate the results.In the fourth chapter, a chemostat model of two delays with one singlemicroorganism competing one limiting substrate is considered, one delay describes thetime in the conversion of nutrient consumed to viable biomass, and the other delaymodels the fact that the nutrient is partially recycled after the death of the bio mass bybacterial decomposition. By analyzing the surmounting multinomial secular equationwith delay-dependent coefficients, the conditions for the asymptotic stability of the unique nontrivial positive steady state of the model and the appearance of periodicsolutions are obtained. Computer simulations illustrate the results.