Coexistence And Output Optimization Analysis And Numerical Simulation Of Two Microbial Competitive System Based On Nutrient Consumption

Biologists have already established a mathematical model for many life phenomena, the model is mainly the chemostat constant in the continuous cultivation of microbial populations, although there are a lot of researches on the model of the competitive system of variable consumption rate, in high nutrient concentration the model of the consumption rate of microorganism is less sensitive to the nutrient concentration is few. In this paper, we mainly study the competition chemosat modelof the rate of microbial consumption of the more sensitive to the nutrient concentration.In this paper, firstly through analyzing the competitive model of the two variable consumpion rate with the inequal growth function, the absence of internal equilibrium point is obtained, under certain conditions, one of the microorganisms is extinct, and there is a stable equilibrium point or a stable limit cycle on the two-dimensional manifold of the microorganism and nutrition, the principle of competitive exclusion was established. Then the numerical simulation is carried out to verify the conclusion.Secondly, through analyzing the competitive model of the two variable consumpion rate with the equal growth function, under certain conditions, the absence of internal equilibrium point is obtained, the internal equilibrium point is obtained, and the two kinds of microorganisms can coexist, at the same time, through numerical simulation of the model, get model parameters satisfy certain conditions, the quantity of microorganism in the initial input selection is different, the microbes of the final output or tend to a stable equilibrium point of internal, or tends to a stable limit within the ring, which is a new attraction structure.Finally, through numerical simulating the competitive model of the two variable consumpion rate with the equal growth function, according to the simulation results, further analysis of the effect of model parameters on microbial quantity of output, obtaining the existence of the parameters to achieve the optimal output of microorganisms.