A model of allelopathy in the context of bacteriocin production

Applied Mathematics and Computation

Volumn 183, Issue 2, 2006, Pages 916-931

  Abell, Martha ^a   Braselton, James ^a   Braselton, Lorraine ^a  

^a GEORGIA SOUTHERN UNIVERSITY   (United States)

Author keywords

Allelopathy; Bacteriocin; Chemostat; Competition; Dulac criterion; Mutation; Routh Hurwitz

Indexed keywords

FOOD PROCESSING; MATHEMATICAL MODELS; TOXIC MATERIALS;

ALLELOPATHY; BACTERIOCIN; CHEMOSTAT; DULAC CRITERION; MUTATION; ROUTH-HURWITZ;

BACTERIA;

EID: 33845805800     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.06.038     Document Type: Article

References (17)

1. Frederickson A.G., and Stephanopoulos G. Microbial Competition. Science 213 (1981) 972
2. H.L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Math. Surv. and Monographs, No. 41. AMS, Providence, RI, 1995.
3. Hsu S.B., Hubbell S.P., and Waltman P. A mathematical theory for single nutrient competition in continuous cultures of micro-organisms. SIAM J. Appl. Math. 32 (1977) 366-383
4. Smith H.L., and Waltman P. The theory of the chemostat: dynamics of microbial competition. Cambridge Stud. Math. Biol. (1995), Cambridge University Press
5. Hansen S.R., and Hubbell S.P. Single nutrient microbial competition: agreement between experimental and theoretical forecast outcomes. Science 20 (1980) 1491
6. Hsu S.B., and Waltman P. A survey of mathematical models of competition with an inhibitor. Math. Biosci. 87 (2004) 53-91
7. Hsu S.B., and Waltman P. Competition in the chemostat when one competitor produces a toxin. Jpn. J. Ind. Appl. Math. 15 (1998) 471-490
8. Braselton J.P., and Waltman P. A competition model with dynamically allocated inhibitor production. Math. Biosci. 52 (2001) 23-35
9. Riley M.A. Molecular mechanisms of bacteriocin evolution. Annu. Rev. Genet. 32 (1998) 255-278
10. Frank S.A. Spatial polymorphism of bacteriocins and other allelopathic traits. Evolution. Ecol. 8 (1994) 369-386
11. Dykes G.A., and Hastings J.W. Selection and fitness in bacteriocin-producing bacteria. Proc. R. Soc. London Ser. B 264 (1997) 683-687
12. Thieme H.R. Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations. J. Math. Biol. 30 (1992) 755-763
13. Hsu S.B., Waltman P., and Wolkowicz G.S.K. Global analysis of a model of plasmid-bearing, plasmid-free competition in a chemostat. J. Math. Biol. 32 (1994) 731-742
14. Merkin D.R. Introduction to the Theory of Stability (1997), Springer-Verlag, New York
15. Glendinning P. Stability, Instability and Chaos: an Introduction to the Theory of Nonlinear Differential Equations (1994), Cambridge University Press, Cambridge
16. Jordan D.W., and Smith P. Nonlinear Ordinary Differential Equations: an Introduction to Dynamical Systems. Third ed. (1999), Oxford University Press, Oxford
17. Bowers R.G. A baseline model for the apparent competition between many host strains: the evolution of host resistance to microparasites. J. Theor. Biol. 200 (1999) 65-75