1. Hopf bifurcation of a five-dimensional delay differential system.
- Author
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Li, Xiaofang, Qu, Rongning, and Feng, Enmin
- Subjects
- *
BIFURCATION theory , *HOPF algebras , *DELAY differential equations , *DIMENSIONAL analysis , *OSCILLATION theory of difference equations , *ALGORITHMS , *STABILITY (Mechanics) - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2011
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