A note on competition in the bioreactor with toxin
- 82 Downloads
In this paper, we investigate a model with yields: γ1 = A 1 + B 1 S m and γ2 = A 2 + B 2 S n , for the competition in the bioreactor of two competitors for a single nutrient, in which one of the competitors produces toxin against its opponent. The existence of limit cycles in the 3-D system is obtained by using a Hopf bifurcation.
KeywordsBioreactor variable yields toxin bifurcation limit cycles
AMS subject classification34C35 34D20 92D25
- 1.Smith H.L., Waltman P. (1995). The Theory of the Chemostat. Cambridge University, Cambridge, UKGoogle Scholar
- 8.Arino J., Pilyugin S.S., Wolkowicz G.K. (2003). Considerations on yield, nutrient uptake, cellular, and competition in chemostat models. Can. Appl. Math. Q. 11(2):107–142Google Scholar
- 18.Zhang J. (1987). The Geometric Theory and Bifurcation Problem of Ordinary Differential Equation. Peking University press, BeijingGoogle Scholar