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论文类型：期刊论文
发表时间：2011-01-01
发表刊物：INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
收录刊物：SCIE
卷号：88
期号：1
页面范围：79-96
ISSN号：0020-7160
关键字：delay; Hopf bifurcation; stability; periodic solution; oscillation
摘要：A five-dimensional delay differential system is proposed to describe oscillatory behaviour in microbial continuous culture. Stability and Hopf bifurcation are discussed, including the changing regularity of the bifurcation value. An explicit algorithm for determining the direction of Hopf bifurcation and the stability of periodic solution is derived, using the theory of normal form and centre manifold. Finally, some numerical simulations are performed to illustrate the analytical results found.