Spatial Dynamics Of A Periodic Unstirred Chemostat Model With Delay

The chemostat is a basic piece of laboratory apparatus and it played an important role in ecology. It is a continuous culture device of constant volume for microorganisms into which a nutrient medium is pumped, balanced by an outflow that removes nutrients and organisms. Generally, for the microorganism, the delay is often caused by the conversion of consumed nutrient into itself. In addition, the nutrient concentration in the medium is maintained at the periodically varying concentration at the up stream end of the channel. Therefore, it is of importance to study the periodic unstirred chemostat model with delay. This thesis is devoted to spatial dynamics of a periodic and delayed reaction-advection-diffusion chemostat model. The main contents are as follows.Firstly, taking the periodicity, diffusion and delay into consideration, we derive a delayed reaction-advection-diffusion system with periodic boundary condition.Secondly, we study the single resource —— the single population model. By using the theory of dynamical system and semigroup, we investigate the current model system. Through verifying the quasi-positive condition, the existence and uniqueness of the global solution of the system is shown. Moreover, we present the sufficient conditions of the uniform persistence of the system.Finally, we study the single resource —— two competing populations model.By virtue of the analysis of the spectral radius of the Poincar′e map of the associated linear delayed reaction-advection-diffusion equation, we show the competitive exclusion principle for the model system. Furthermore, the sufficient conditions of the coexistence of two competing population are established.