Feedback-mediated oscillatory coexistence in the chemostat

Lecture Notes in Control and Information Sciences

Volumn 341, Issue , 2006, Pages 97-104

  De Leenheer, Patrick ^a   Pilyugin, Sergei S ^a  

^a UNIVERSITY OF FLORIDA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33750186269     PISSN: 01708643     EISSN: None     Source Type: Book Series    
DOI: 10.1007/11757344_13     Document Type: Article

References (17)

1. J. ARINO, S. S. PILYUGIN, AND G.S.K. WOLKOWICZ, Considerations on yield, nutrient uptake, cellular growth, and competition in chemostat models, Can. Appl. Math. Quart. 11 (2003), pp. 107-142.
2. G. J. BUTLER AND P. WALTMAN, Bifurcation from a limit cycle in a two-predator-one prey ecosystem modeled on a chemostat, J. Math. Biol. 12 (1981), pp. 295-310.
3. G. J. BUTLER, S. B. HSU, AND P. WALTMAN, Coexistence of competing predators in a chemostat, J. Math. Biol. 17 (1983), pp. 133-151.
4. G. J. BUTLER, S. B. HSU, AND P. WALTMAN, A mathematical model of the chemostat with periodic washout rate, SIAM J. Appl. Math. 45 (1985), pp. 435-449.
5. G. J. BUTLER AND G.S.K. WOLKOWICZ, A mathematical model of the chemostat with general class of functions describing nutrient uptake, SIAM J. Appl. Math. 45 (1985), pp. 138-151.
6. P. DE LEENHEER AND H. L. SMITH, Feedback control for chemostat models, J. Math. Biol. 46 (2003), pp. 48-70.
7. P. DE LEENHEER, B. LI, AND H.L. SMITH, Competition in the chemostat: some remarks, Can. Appl. Math. Quart. 11 (2003), pp. 229-248.
8. S.F. ELLERMEYER, S.S. PILYUGIN, AND R. REDHEFFER, Persistence criteria for a chemostat with variable nutrient input, J. Differential Equations 171 (2001), pp. 132-147.
9. J.-L. GOUZÉ AND G. ROBLEDO, Feedback control for nonmonotone competition models in the chemostat, Nonlinear Analysis: Real World Applications 6 (2005), pp. 671-690.
10. J. K. HALE AND A.S. SOMOLINOS, Competition for fluctuating nutrient, J. Math. Biol. 18 (1983), pp. 255-280.
11. S. B. HSU, Limiting behavior of competing species, SIAM J. Appl. Math. 34 (1978), pp. 760-763.
12. S. S. PILYUGIN AND P. WALTMAN, Multiple limit cycles in the chemostat with variable yield, Math. Biosci. 182 (2003), pp. 151-166.
13. S. S. PILYUGIN AND P. WALTMAN, Divergence criterion for generic planar systems, SIAM J. Appl. Math. 64 (2003), pp. 81-93.
14. N.S. RAO AND E. O. ROXIN, Controlled growth of competing species, SIAM J. Appl. Math. 50 (1990), pp. 853-864.
15. H.L. SMITH, Competitive coexistence in an oscillating chemostat, SIAM J. Appl. Math. 40 (1981), pp. 498-522.
16. H.L. SMITH AND P. WALTMAN, The Theory of the Chemostat, Cambridge University Press, Cambridge, 1995.
17. G.S.K. WOLKOWICZ AND Z. LU, Global dynamics of a mathematical model of competition in the chemostat: general response functions and differential death rates, SIAM J. Appl. Math. 48 (1992), pp. 222-233.