| Title:
|
Differential growth models for microbial populations (English) |
| Author:
|
Milota, Jaroslav |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
27 |
| Issue:
|
1 |
| Year:
|
1982 |
| Pages:
|
1-16 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
Two models of microbial growth are derived as a resuslt of a discussion of the models of Monod and Hinshelwood types. The approach takes account of the lyse of dead cells in inhibitory products as well as in those which stimulate the growth. The asymptotic behaviour of the models is proved and the models applied to a chemostat. (English) |
| Keyword:
|
differential growth models |
| Keyword:
|
microbial populations |
| Keyword:
|
asymptotic behaviour |
| Keyword:
|
chemostat |
| Keyword:
|
deterministic models |
| Keyword:
|
Monod model |
| Keyword:
|
new three component model |
| Keyword:
|
live cells |
| Keyword:
|
toxins |
| Keyword:
|
nutrients |
| Keyword:
|
bifurcation |
| Keyword:
|
stability of limit cycles |
| MSC:
|
34C05 |
| MSC:
|
92A15 |
| MSC:
|
92D25 |
| idZBL:
|
Zbl 0495.92016 |
| idMR:
|
MR0640136 |
| DOI:
|
10.21136/AM.1982.103941 |
| . |
| Date available:
|
2008-05-20T18:18:13Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103941 |
| . |
| Reference:
|
[1] T. D. Brock: Microbial Ecology.Englewood Cliffs, Prentice Hall (1966). |
| Reference:
|
[2] V. H. Edwards: The influence of high substrate concentration on microbial kinetics.Biotechnol. Bioeng. 12 (1970), 679-691. 10.1002/bit.260120504 |
| Reference:
|
[3] Z. Fencl: A theoretical analysis of continuous culture system.In "Theoretical Basis of Continuous Culture of Microorganisms". Publ. House Czech. Acad. Sci., Prague (1966). |
| Reference:
|
[4] R. K. Finn: Inhibitory all products.J. Perm. Techn. 44 (1966), 305-321. |
| Reference:
|
[5] R. I. Fletcher: A general solution for the complete Richards function.Math. Biosci. 27 (1975), 349-360. Zbl 0324.92006, 10.1016/0025-5564(75)90112-1 |
| Reference:
|
[6] D. Herbert R. Elsworth R. C. Telling: Continuous culture of bacteria.J. Gen. Microbiol. 14 (1956), 601-621. 10.1099/00221287-14-3-601 |
| Reference:
|
[7] S. N. Hinshelwood: The Chemical Kinetics of the Bacterial Cell.Oxford Univ. Press, 1946. |
| Reference:
|
[8] N. D. Jerusalemskii: Control principles for microbial growth.In "Control of Biosynthesis", Moscow 1966 (Russian). |
| Reference:
|
[9] E. V. Kuzmin: Remark on a growth curve for microbial populations.In "Control of Microbial Cultivation", Moscow 1969 (Russian). |
| Reference:
|
[10] J. E. Marsden M. McCracken: The Hopf Bifurcation and its Applications.Springer Verlag, New York-Heidelberg-Berlin, 1976. MR 0494309 |
| Reference:
|
[11] R. M. May G. R. Conway M. P. Hassell T. R. E. Southwood: Time delays, density dependence and single species oscillations.J. Anim. Ecol. 43 (1974), 747-770. 10.2307/3535 |
| Reference:
|
[12] J. Monod: Le Croissance des Cultures Bacteriennes.Hermann et Cie, Paris, 1942. |
| Reference:
|
[13] H. Moser: The Dynamics of Bacterial Populations Maintained in the Chernostat.Washington Carneige Publ., 1958. |
| Reference:
|
[14] G. Oster J. Guckenheimer: Bifurcation phenomena in population models.pp. 327-353 in [10]. |
| Reference:
|
[15] E. O. Powell: Theory of the chernostat.Lab. Practice 14 (1965), 1145-1158. |
| Reference:
|
[16] F. M. Scuodo J. R. Ziegler: The Golden Age of Theoretical Ecology: 1923-1940.Lecture Notes in Biomathematics No 22, Springer Verlag, Berlin-Heidelberg-New York, 1978. MR 0521933 |
| Reference:
|
[17] G. Teissier: Kinetics behaviour of heterogeneous populations in completely mixed reactors.Ann. Physiol. Biol. 12, 527-586. |
| Reference:
|
[18] F. M. Williams: A model of cell growth dynamics.J. Theor. Biol. 15 (1967), 190-207. 10.1016/0022-5193(67)90200-7 |
| Reference:
|
[19] T. B. Young D. F. Bruley H. R. Bungay III: A dynamic mathematical model of the chemostat.Biotechnol. Bioeng. 15 (1970), 747-769. |
| . |
