Complex dynamics of a chemostat with variable yield and periodically impulsive perturbation on the substrate

Journal of Mathematical Chemistry

Volumn 43, Issue 1, 2008, Pages 338-349

  Sun, Shulin ^a,b   Chen, Lansun ^b  

^a SHANXI NORMAL UNIVERSITY   (China)

^b DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Chaotic attractor; Periodically pulsed substrate; Permanence; Variable yield

Indexed keywords

EID: 37549018909     PISSN: 02599791     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10910-006-9200-z     Document Type: Article

References (18)

1. Smith H.L., Waltman P., (1995) The Theory of the Chemostat. Cambridge University Press, Cambridge UK
2. Novick A., Szilard L., (1950) Description of the chemostat. Science 112: 715-716
3. Herbert D., Elsworth R., Telling R.C., (1956) The continuous culture of bacteria: a theoretical and experimental study. J. Gen. Microbiol. 14: 601-622
4. Hsu S.B., Hubbell S.P., Waltman P., (1977) A mathematical theory for single nutrient competition in continuous cultures of micro-organisms. SIAM J. Appl. Math. 32: 366-383
5. Hale J.K., Somolinas A.S., (1983) Competition for fluctuating nutrient. J. Math. Biol. 18: 255-280
6. Buler G.J., Hsu S.B., Waltman P., (1985) A mathematical model of the chemostat with periodic washout rate. SIAM J. Appl.Math. 45: 435-449
7. Wolkowicz G.S.K., Zhao X.Q., (1998) N-spicies competition in a periodic chemostat. Diff Integral Eqs. 11: 465-491
8. Crooke P.S., Wei C.J., Tanner R.D., (1980) The effect of the specific growth rate and yield expressions on the existence of oscillatory behavior of a continuous fermentation model. Chem. Eng. Commun. 6: 333-347
9. Crooke P.S., Tanner R.D., (1982) Hopf bifurcation for a variable yield continuous fermentation model. Int. J. Eng. Sci. 20: 439-443
10. Agrawal R., Lee C., Lim H.C., Ramkrishna D., (1982) Theoretical investigations of dynamic behavior of isothermal continuous stirred tank biological reactor. Chem. Eng. Sci. 37: 453-462
11. Pilyugin S.S., Waltman P., (2003) Multiple limit cycles in the chemostat with variable yield. Math. Biosci. 182: 151-166
12. Zhu L.M., Huang X.C., (2005) Relative positions of limit cycles in the continuous culture vessel with variable yield. J. Math. Chem. 38: 119-128
13. Lakshmikantham V., Bainov D.D., Simeonov P.S., (1989) Theory of Impulsive Differential Eqations. World Scientific, Singapore
14. Bainov D.D., Simeonov P.S., (1993) Impulsive Differential Eqations: Periodic Solutions and Applications. Longman Scientific and Technical, Burnt Mill
15. Liu X.N., Chen L.S., (2003) Complex dynamics of Holling type II Lotka-Volterra predator-prey system with impulsive perturbations on the predator, Chaos. Solitons Fract. 16: 311-320
16. Ballinger G., Liu X., (1997) Permanence of population growth models with impulsive effects. Math. Comput. Model. 26: 59-72
17. Funasaki E., Kot M., (1993) Invasion and chaos in a periodically pulsed mass-action chemostat. Theor. Popul. Biol. 44: 203-224
18. Smith R.J., Wolkowicz G.S.K., (2004) Analysis of a model of the nutrient driven self-cycling fermentation process. Dyn. Contin. Discrete Impul. Syst. Ser. B, 11: 239-265