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Stability of nonlinear microbial bioconversion system concerning glycerol’s active transport and 1,3-PD’s passive transport. (English) Zbl 1205.34057

Summary: A new nonlinear mathematical model is developed to describe the conversion of glycerol to 1,3- propanediol by Klebsiella pneumoniae and the changes of concentrations of intracellular substances are taken into consideration. We consider the cases that glycerol passes the membrane by active transport and 1,3-propanediol passes the membrane by passive transport. We firstly study the existence and uniqueness of a solution and prove that the solution is bounded in a positive quadrant. Secondly, we discuss the existence of equilibrium solutions and calculate them, depending on some given steady accuracy by Newton’s method. Lastly, we analyze the asymptotical behavior and the global stability of the mathematical model.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
34D20 Stability of solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
92C40 Biochemistry, molecular biology
92E99 Chemistry
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