Dynamic Modeling And Study On The Continuous Culture Of Microorganisms Under The Influence Of Noise

Taking the fact that the process of the continuous culture of microorganisms in the chemostat is inevitably affected by environmental noise into consideration,in this thesis,we construct several different kinds of stochastic chemostat models using the relative theories of stochastic differential equations,including simple stochastic chemostat models with white or colour noise,multi-species competition stochastic chemostat models with white noise,and two-species competition stochastic chemostat models with feedback control.Mainly,we analyze the conditions under which the microorganisms persist or become extinct in the chemostat,and discuss the effect of noise on the destiny of the microorganisms.More precisely,the results of this thesis are as follows:First of all,we develop and analyse a simple stochastic chemostat model in which the dilution rate is influenced by white noise.The conditions under which the washout equilibrium is stochastically asymptotically stable in the large and the solution spirals around the positive equilibrium of its corresponding deterministic model are obtained.It is found that large noise can make the microorganism go extinct in the chemostat.We further consider two simple stochastic chemostat models in which the maximal growth rate is influenced by white noise or experiences sudden instantaneous switching.By defining a stochastic break-even concentration and an average break-even concentration,the threshold dynamics for the two stochastic chemostat models are respectively investigated.Secondly,we construct two competitive stochastic chemostat models with multiple microorganism species,where the specific per-capita substrate uptake rates of the microorganism species are linear functions or continuously differentiable and monotone increasing functions.Asymptotic pathwise estimations of the stochastic models are first performed.By defining a stochastic break-even concentration for each species,we prove that the competitive exclusion principle holds for the stochastic competition chemostat models.In other words,the species with the lowest stochastic break-even concentration survives and all other species will go to extinction in the chemostat.Moreover,we find that noise may change the destiny of the microorganism species in the chemostat.Finally,for the case that the maximal specific growth rates of the microorganisms are affected by white noise,we present three two-species competition stochastic chemostat models with respectively feedback control,inhibitory nutrients and obligatemutualistic species.Using the technique of stochastic sensitivity functions,we construct the confidence domains of the stochastic attractors(confidence ellipse and confidence band)which allow us to analyze the dispersion of the random states around the corresponding deterministic attractor.With the help of the confidence domain and the separatrix of attraction basins of the corresponding deterministic model,we estimate the critical value of the intensity for the noise generating a transition from coexistence to extinction,and propose some feedback control strategies which can prevent the noise-induced extinction.