Abstract
Based on 1,3-propanediol production from continuous fermentation of glycerol by Klebsiellapneumoniae, the dynamic behaviors of a kinetics system with continuous time-delay are analyzed. At first, a six-dimension kinetics system concerning the intracellular substance is proposed by introducing weak nuclear continuous time-delay into the specific cellular growth rate. Second, taking the inverse of average time-delay as parameter, the local stability of the positive equilibriums and the existence of Hopf bifurcation are discussed. Finally, the period solution of biomass and the parameter region of Hopf bifurcation are pictured numerically taking some special number in substrate concentration in feed medium and dilution rate.
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