Differential growth models for microbial populations

Jaroslav Milota

Aplikace matematiky (1982)

  • Volume: 27, Issue: 1, page 1-16
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Milota, Jaroslav. "Differential growth models for microbial populations." Aplikace matematiky 27.1 (1982): 1-16. <http://eudml.org/doc/15220>.

@article{Milota1982,
abstract = {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.},
author = {Milota, Jaroslav},
journal = {Aplikace matematiky},
keywords = {differential growth models; microbial populations; asymptotic behaviour; chemostat; deterministic models; Monod model; new three component model; live cells; toxins; nutrients; bifurcation; stability of limit cycles; differential growth models; microbial populations; asymptotic behaviour; chemostat; deterministic models; Monod model; new three component model; live cells; toxins; nutrients; bifurcation; stability of limit cycles},
language = {eng},
number = {1},
pages = {1-16},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Differential growth models for microbial populations},
url = {http://eudml.org/doc/15220},
volume = {27},
year = {1982},
}

TY - JOUR
AU - Milota, Jaroslav
TI - Differential growth models for microbial populations
JO - Aplikace matematiky
PY - 1982
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 27
IS - 1
SP - 1
EP - 16
AB - 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.
LA - eng
KW - differential growth models; microbial populations; asymptotic behaviour; chemostat; deterministic models; Monod model; new three component model; live cells; toxins; nutrients; bifurcation; stability of limit cycles; differential growth models; microbial populations; asymptotic behaviour; chemostat; deterministic models; Monod model; new three component model; live cells; toxins; nutrients; bifurcation; stability of limit cycles
UR - http://eudml.org/doc/15220
ER -

References

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  1. T. D. Brock, Microbial Ecology, Englewood Cliffs, Prentice Hall (1966). (1966) 
  2. V. H. Edwards, 10.1002/bit.260120504, Biotechnol. Bioeng. 12 (1970), 679-691. (1970) DOI10.1002/bit.260120504
  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). (1966) 
  4. R. K. Finn, Inhibitory all products, J. Perm. Techn. 44 (1966), 305-321. (1966) 
  5. R. I. Fletcher, 10.1016/0025-5564(75)90112-1, Math. Biosci. 27 (1975), 349-360. (1975) Zbl0324.92006DOI10.1016/0025-5564(75)90112-1
  6. D. Herbert R. Elsworth R. C. Telling, 10.1099/00221287-14-3-601, J. Gen. Microbiol. 14 (1956), 601-621. (1956) DOI10.1099/00221287-14-3-601
  7. S. N. Hinshelwood, The Chemical Kinetics of the Bacterial Cell, Oxford Univ. Press, 1946. (1946) 
  8. N. D. Jerusalemskii, Control principles for microbial growth, In "Control of Biosynthesis", Moscow 1966 (Russian). (1966) 
  9. E. V. Kuzmin, Remark on a growth curve for microbial populations, In "Control of Microbial Cultivation", Moscow 1969 (Russian). (1969) 
  10. J. E. Marsden M. McCracken, The Hopf Bifurcation and its Applications, Springer Verlag, New York-Heidelberg-Berlin, 1976. (1976) Zbl0346.58007MR0494309
  11. R. M. May G. R. Conway M. P. Hassell T. R. E. Southwood, 10.2307/3535, J. Anim. Ecol. 43 (1974), 747-770. (1974) DOI10.2307/3535
  12. J. Monod, Le Croissance des Cultures Bacteriennes, Hermann et Cie, Paris, 1942. (1942) Zbl0063.04097
  13. H. Moser, The Dynamics of Bacterial Populations Maintained in the Chernostat, Washington Carneige Publ., 1958. (1958) 
  14. G. Oster J. Guckenheimer, Bifurcation phenomena in population models, pp. 327-353 in [10]. Zbl0379.92016
  15. E. O. Powell, Theory of the chernostat, Lab. Practice 14 (1965), 1145-1158. (1965) 
  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. (1978) MR0521933
  17. G. Teissier, Kinetics behaviour of heterogeneous populations in completely mixed reactors, Ann. Physiol. Biol. 12, 527-586. 
  18. F. M. Williams, 10.1016/0022-5193(67)90200-7, J. Theor. Biol. 15 (1967), 190-207. (1967) DOI10.1016/0022-5193(67)90200-7
  19. T. B. Young D. F. Bruley H. R. Bungay III, A dynamic mathematical model of the chemostat, Biotechnol. Bioeng. 15 (1970), 747-769. (1970) 

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