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论文类型：期刊论文
发表时间：2009-10-01
发表刊物：NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
收录刊物：SCIE、EI、Scopus
卷号：10
期号：5
页面范围：2749-2757
ISSN号：1468-1218
关键字：Time delay; Hopf bifurcation; Stability; Periodic solution; Phase plane
摘要：By introducing discrete time delay into the model for producing 1,3-propanediol by microbial continuous fermentation, we consider the stability and Hopf bifurcation of the delay differential system. Through numerical simulations, we get the rule of branch value changing with parameter and draw the pictures of periodic solutions and phase diagrams with specified parameters. The effect of time delay suggests that the system can qualitatively describe oscillatory phenomena occurring in the experiment. (C) 2008 Elsevier Ltd. All rights reserved.