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Date:2019-03-09

Indexed by:Journal Article

Date of Publication:2010-10-01

Journal:NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS

Included Journals:Scopus、EI、SCIE

Volume:11

Issue:5

Page Number:3501-3511

ISSN:1468-1218

Key Words:1,3-propanediol; Transport across cell membrane; Intracellular substances; Equilibrium solution; Stability

Abstract:In this study, 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 solution's existence and uniqueness and prove that the solution is bounded in a positive quadrant. Secondly, we discuss the existence of equilibrium solutions and calculate them, dependent on some given steady accuracy by Newton's Method. Lastly, we analyze the asymptotical behavior and the global stability of the mathematical model. (C) 2009 Elsevier Ltd. All rights reserved.