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- Title
Delay induced oscillations in a turbidostat with feedback control.
- Authors
Yuan, Sanling; Li, Pan; Song, Yongli
- Abstract
A model of competition between two species in a turbidostat with delayed feedback control is investigated. By choosing the delay in the measurement of the optical sensor to the turbidity of the fluid as a bifurcation parameter, we show that Hopf bifurcations can occur as the delay crosses some critical values. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem. Computer simulations illustrate the results.
- Subjects
FEEDBACK control systems; COMPETITION (Biology); OSCILLATIONS; BIFURCATION theory; COMPUTER simulation; TURBIDITY; HOPF algebras; STABILITY (Mechanics)
- Publication
Journal of Mathematical Chemistry, 2011, Vol 49, Issue 8, p1646
- ISSN
0259-9791
- Publication type
Article
- DOI
10.1007/s10910-011-9848-x