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Indexed by:期刊论文

Date of Publication:2011-01-01

Journal:INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS

Included Journals:SCIE

Volume:88

Issue:1

Page Number:79-96

ISSN No.:0020-7160

Key Words:delay; Hopf bifurcation; stability; periodic solution; oscillation

Abstract: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.