Global asymptotic behavior of a chemostat model with delayed response in growth

Applied Mathematics and Computation

Volumn 147, Issue 1, 2004, Pages 147-161

  El Owaidy, H M ^a   Moniem, A A ^b  

^a Assiut Branch   (Egypt)

^b Akhbar El Yom Academy   (Egypt)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; FUNCTIONS; MATHEMATICAL MODELS;

AUXILIARY FUNCTIONS;

CHEMOSTATS;

EID: 0141748139     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(02)00658-6     Document Type: Article

References (9)

1. Bush A.W., Cook A.E. The effect of time delay and growth rate inhibition in the bacterial treatment of wastewater. J. Theor. Biol. 63:1975;385-395.
2. Hsu G.B., Hubbell S., Waltman P. A mathematical theory for single-nutrient competition in continuous cultures of microorganisms. SIAM J. Appl. Math. 32:1977;366-383.
3. Butler G.J., Wolkowicz G.S. A mathematical model of the chemostat with a general class of functions describing nutrient uptake. SIAM J. Appl. Math. 45:1985;138-151.
4. Freedman H.I., So J.W.H., Waltman P. Chemostat competition with time delays. Vichnevetsky R., Borne P., Vignes J. Proceeding of IMACS (1988): 12th World Congress on Scientific Computation: Modeling and Simulation of System Paris. 1988;102-104 Gerfidn Cite Scientifique, France.
5. Freedman H.I., So J.W.H., Waltman P. Coexistence in a model of competition in the chemostat incorporating discrete delays. SIAM J. Appl. Math. 49:1989;859-870.
6. Smith H.L., Waltman P. The Theory of Chemostat. 1995;Cambridge University Press, Cambridge, UK.
7. El-Owaidy H.M., Ismail M. Asymptotic behavior of the chemostat model with delayed response in growth. Chaos, Solitons Fract. 13:2002;787-795.
8. Ellermeyer S.F. Competition in the chemostat: global asymptotic behavior of a model with delayed response in growth. SIAM J. Appl. Math. 54:1994;456-465.
9. Wendi W., Zhien M. Converges in the chemostat model with delayed response in growth. J. Syst. Sci. Math. Sci. 12:1999;23-32.