Periodic solutions in a model of competition between plasmid-bearing and plasmid-free organisms in a chemostat with an inhibitor

Journal of Mathematical Biology

Volumn 42, Issue 1, 2001, Pages 71-94

  Ai, Shangbing ^a  

^a UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

Brouwer fixed point theorem; Chemostat; Periodic solution

Indexed keywords

ANTIINFECTIVE AGENT;

ANTIBIOTIC RESISTANCE; ARTICLE; BIOLOGICAL MODEL; BIOREACTOR; GENETIC ENGINEERING; GENETICS; MATHEMATICAL COMPUTING; METABOLISM; PERIODICITY; PLASMID;

ANTI-BACTERIAL AGENTS; BIOREACTORS; DRUG RESISTANCE, MICROBIAL; GENETIC ENGINEERING; MATHEMATICAL COMPUTING; MODELS, BIOLOGICAL; MODELS, GENETIC; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; PERIODICITY; PLASMIDS;

EID: 0035236141     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00000073     Document Type: Article

References (14)

1. Hsu, S.B., Luo, T.-K., Waltman, P.: Competition between plasmid-bearing organisms in a chemostat with an inhibitor, J. Math. Biol., 34, 225-238 (1995)
2. Hastings, S.P., Murray, J.D.: The existence of oscillatory solutions in the Field-Noyes model for The Belousov-Zhabotinskii reaction, SIAM J. Appl. Math., 28, 678-688 (1975)
3. Hsu, S.B., Waltman, P.: Analysis of a model of two competitors in a chemostat with an external inhibitor, SIAM J. Appl. Math., 52, 528-540 (1992)
4. Smith, H.L.: Periodic orbits of competitive and cooperative systems, J. Diff. Eq. 65, 361-373 (1986)
5. Smith, H.L.: On the basin of attraction of a perturbed attractor, Nonlinear Analysis, Theory, Methods and Applications 6, 911-917 (1982)
6. Smith, H.L., Waltman, P.: The theory of the chemostat: dynamics of the microbial competition, Cambridge University Press, Cambridge (1995)
7. Stephanopoulis, G., Lapidus, G.: Chemostat dynamics of plasmid-bearing plasmid-free mixed recombinant cultures, Chem. Engr. Science, 43, 49-57 (1988)
8. Lenski, R.E., Hattingh, S.: Coexistence of two competitors in one resource and one inhibitor: a chemostat model based on bacteria and antibiotics, J. Theoretical Biol. 122, 83-93 (1986)
9. Waltman, P.: Coexistence in chemostat-like models, Rocky Mount. J. Math, 20, 777-807 (1990)
10. Stephanopoulis, G., San, K.Y., Davidson, B.H.: A novel bioreactor-cell precipitator combination for high-cell density, high flow fermentations, Biotecnology Progress 4, 250-259 (1985)
11. Macken, C.A., Levin, S.A., Walttatter, S.A.: The dynamics of bacteria-plasmid systems, Mathematical Biosciences, 32, 123-145 (1994)
12. Simonsen, L.: The existence conditions for bacterial plasmids: theory and reality, Microbial Ecology, 22, 187-205 (1991)
13. Frederickson, A.G., Stephanopoulis, G.: Microbial competition, Science 213, 972-979 (1981)
14. Monod, J.: Recherches sur la croissance des cultures bacteriennes, Paris: Herman