Analysis Of Positive Solutions For A Multiple Food Chain Model In An Unstirred Chemostat

Abstract chemostat (often called a continuous culture) is usually served as a reactor widely used in microorganisms culture, waste treatment, biology pharmacy and food processing etc. We can reach expected goals by controlling concentration of microorganisms or adjusting some parameters in the system. Depending on mathematical methods to model, analyze, control, and optimize the system, there are very important significances in the reactor designing and the cost of product decreasing.In this paper, an unstirred multiple food chain chemostat model with Michaelis-Menten or Beddington-DeAngelis functional response is discussed. There are a nutrient, two competing species and a predator population in the system, where the competing species concentrations is changing with the concentration of nutrient and predator. The chemostat model takes the form mathematically as followings:with boundary conditionsand initial conditionswhere fi(p, q) = p/(1 + αip+ βiq). S(x, t), u(x, t), v(x, t), w(x, t) are the concentrations of the nutrient, species respectively. The parameters m1,m2 and m3 are the maximal bith rate of u,v and w, respectively, αi > 0,βi≥0,i = 1,2,3.