-
2
-
-
0017386947
-
Dynamics of a chemostat in which two organisms compete for a common substrate
-
Aris R., Humphrey A.E. Dynamics of a chemostat in which two organisms compete for a common substrate. Biotechnol. Bioeng. 19:1977;1375.
-
(1977)
Biotechnol. Bioeng.
, vol.19
, pp. 1375
-
-
Aris, R.1
Humphrey, A.E.2
-
3
-
-
0022012911
-
A mathematical model of the chemostat with a general class of functions describing nutrient uptake
-
Butler G.J., Wolkowicz G.S.K. A mathematical model of the chemostat with a general class of functions describing nutrient uptake. SIAM J. Appl. Math. 45:1985;138.
-
(1985)
SIAM J. Appl. Math.
, vol.45
, pp. 138
-
-
Butler, G.J.1
Wolkowicz, G.S.K.2
-
4
-
-
0000468175
-
Limiting behavior for competing species
-
Hsu S.B. Limiting behavior for competing species. SIAM J. Appl. Math. 34:1978;760.
-
(1978)
SIAM J. Appl. Math.
, vol.34
, pp. 760
-
-
Hsu, S.B.1
-
5
-
-
0000875842
-
A mathematical theory for single-nutrient competition in continuous cultures of micro-organisms
-
Hsu S.B., Hubbell S., Waltman P. A mathematical theory for single-nutrient competition in continuous cultures of micro-organisms. SIAM J. Appl. Math. 32:1977;366.
-
(1977)
SIAM J. Appl. Math.
, vol.32
, pp. 366
-
-
Hsu, S.B.1
Hubbell, S.2
Waltman, P.3
-
6
-
-
0000775549
-
Criteria for the growth of contaminants and mutants in continuous culture
-
Powell E.O. Criteria for the growth of contaminants and mutants in continuous culture. J. Gen. Microbiol. 18:1958;259.
-
(1958)
J. Gen. Microbiol.
, vol.18
, pp. 259
-
-
Powell, E.O.1
-
7
-
-
0026818163
-
Global dynamics of a mathematical model of competition in the chemostat: General response functions and differential death rates
-
Wolkowicz G.S.K., Zhiqi L. Global dynamics of a mathematical model of competition in the chemostat: General response functions and differential death rates. SIAM J. Appl. Math. 52:1992;222.
-
(1992)
SIAM J. Appl. Math.
, vol.52
, pp. 222
-
-
Wolkowicz, G.S.K.1
Zhiqi, L.2
-
8
-
-
0018868854
-
Single-nutrient microbial competition: Qualitative agreement between experimental and theoretically forecast outcomes
-
Hansen S.R., Hubbell S.P. Single-nutrient microbial competition: Qualitative agreement between experimental and theoretically forecast outcomes. Science. 207:1980;1491.
-
(1980)
Science
, vol.207
, pp. 1491
-
-
Hansen, S.R.1
Hubbell, S.P.2
-
10
-
-
0014162576
-
Enrichments of aquatic bacteria in continuous culture
-
Jannasch H.W. Enrichments of aquatic bacteria in continuous culture. Arch. Mikrobiol. 59:1967;165.
-
(1967)
Arch. Mikrobiol.
, vol.59
, pp. 165
-
-
Jannasch, H.W.1
-
11
-
-
0015583054
-
Interactions of Tetrahymena pyriformis, Escherichia coli, Azotobacter vinelandii, and glucose in a minimal medium
-
Jost J.L., Drake J.F., Fredrickson A.G., Tsuchiya H.M. Interactions of Tetrahymena pyriformis, Escherichia coli, Azotobacter vinelandii, and glucose in a minimal medium. J. Bacteriol. 113:1973;834.
-
(1973)
J. Bacteriol.
, vol.113
, pp. 834
-
-
Jost, J.L.1
Drake, J.F.2
Fredrickson, A.G.3
Tsuchiya, H.M.4
-
12
-
-
0015103335
-
Effect of dilution rate on the outcome of chemostat mixed culture experiments
-
Meers J.L. Effect of dilution rate on the outcome of chemostat mixed culture experiments. J. Gen. Microbiol. 67:1971;359.
-
(1971)
J. Gen. Microbiol.
, vol.67
, pp. 359
-
-
Meers, J.L.1
-
13
-
-
0023891906
-
Structural instability of the theory of simple competition
-
Powell G.E. Structural instability of the theory of simple competition. J. Theor. Biol. 132:1988;421.
-
(1988)
J. Theor. Biol.
, vol.132
, pp. 421
-
-
Powell, G.E.1
-
14
-
-
0018500981
-
A stochastic analysis of the growth of competing microbiol populations in a continuous biochemical reactor
-
Stephanopoulos G., Aris R., Fredrickson A.G. A stochastic analysis of the growth of competing microbiol populations in a continuous biochemical reactor. Math. Biosci. 45:1979;99.
-
(1979)
Math. Biosci.
, vol.45
, pp. 99
-
-
Stephanopoulos, G.1
Aris, R.2
Fredrickson, A.G.3
-
15
-
-
0022075298
-
A mathematical model for the chemostat with periodic washout rate
-
Butler G.J., Hsu S.B., Waltman P. A mathematical model for the chemostat with periodic washout rate. SIAM J. Appl. Math. 45:1985;435.
-
(1985)
SIAM J. Appl. Math.
, vol.45
, pp. 435
-
-
Butler, G.J.1
Hsu, S.B.2
Waltman, P.3
-
16
-
-
0021071835
-
Competition for fluctuating nutrient
-
Hale J.K., Somolinos A.S. Competition for fluctuating nutrient. J. Math. Biol. 18:1983;255.
-
(1983)
J. Math. Biol.
, vol.18
, pp. 255
-
-
Hale, J.K.1
Somolinos, A.S.2
-
17
-
-
0019152390
-
A competition model for a seasonally fluctuating nutrient
-
Hsu S.B. A competition model for a seasonally fluctuating nutrient. J. Math. Biol. 9:1980;115.
-
(1980)
J. Math. Biol.
, vol.9
, pp. 115
-
-
Hsu, S.B.1
-
18
-
-
0028165836
-
Periodic, quasi-periodic and chaotic coexistence of two competing microbial population in a periodically operated chemostat
-
Lenas P., Pavlou S. Periodic, quasi-periodic and chaotic coexistence of two competing microbial population in a periodically operated chemostat. Math. Biosci. 121:1994;61.
-
(1994)
Math. Biosci.
, vol.121
, pp. 61
-
-
Lenas, P.1
Pavlou, S.2
-
19
-
-
0022499063
-
Bifurcations in a bang-bang controlled mixed culture system
-
Matsubara M., Watanabe N., Hasegawa S. Bifurcations in a bang-bang controlled mixed culture system. Chem. Eng. Sci. 41:1986;523.
-
(1986)
Chem. Eng. Sci.
, vol.41
, pp. 523
-
-
Matsubara, M.1
Watanabe, N.2
Hasegawa, S.3
-
20
-
-
0025700253
-
On the coexistence of competing microbial species in a chemostat under cycling
-
Pavlou S., Kevrekidis I.G., Lyberatos G. On the coexistence of competing microbial species in a chemostat under cycling. Biotechnol. Bioeng. 35:1990;224.
-
(1990)
Biotechnol. Bioeng.
, vol.35
, pp. 224
-
-
Pavlou, S.1
Kevrekidis, I.G.2
Lyberatos, G.3
-
21
-
-
0000513747
-
Competitive coexistence in an oscillating chemostat
-
Smith H. Competitive coexistence in an oscillating chemostat. SIAM J. Appl. Math. 40:1981;498-522.
-
(1981)
SIAM J. Appl. Math.
, vol.40
, pp. 498-522
-
-
Smith, H.1
-
22
-
-
0018519318
-
The growth of competing microbial populations in a CSTR with periodically varying inputs
-
Stephanopoulos G., Fredrickson A.G., Aris R. The growth of competing microbial populations in a CSTR with periodically varying inputs. AIChE J. 25:1979;863.
-
(1979)
AIChE J.
, vol.25
, pp. 863
-
-
Stephanopoulos, G.1
Fredrickson, A.G.2
Aris, R.3
-
23
-
-
0022766321
-
Effect of pH oscillations on a competing mixed culture
-
Davison B.H., Stephanopoulos G. Effect of pH oscillations on a competing mixed culture. Biotechnol. Bioeng. 28:1986;1127.
-
(1986)
Biotechnol. Bioeng.
, vol.28
, pp. 1127
-
-
Davison, B.H.1
Stephanopoulos, G.2
-
24
-
-
0027201602
-
Competition between two microbial populations in a sequencing fed-batch reactor: Theory, experimental verification, and implications for waste treatment applications
-
Dikshitulu S., Baltzis B.C., Lewandowski G.A., Pavlou S. Competition between two microbial populations in a sequencing fed-batch reactor: Theory, experimental verification, and implications for waste treatment applications. Biotechnol. Bioeng. 42:1993;643.
-
(1993)
Biotechnol. Bioeng.
, vol.42
, pp. 643
-
-
Dikshitulu, S.1
Baltzis, B.C.2
Lewandowski, G.A.3
Pavlou, S.4
-
27
-
-
0023533666
-
Operating Parameters' effects on the outcome of pure and simple competition between two populations in configurations of two interconnected chemostats
-
Kung C.-M., Baltzis B.C. Operating Parameters' effects on the outcome of pure and simple competition between two populations in configurations of two interconnected chemostats. Biotechnol. Bioeng. 30:1987;1006.
-
(1987)
Biotechnol. Bioeng.
, vol.30
, pp. 1006
-
-
Kung, C.-M.1
Baltzis, B.C.2
-
28
-
-
0032004317
-
Oscillations of two competing microbial populations in configurations of two interconnected chemostats
-
Lenas P., Thomopoulos N.A., Vayenas D.V., Pavlou S. Oscillations of two competing microbial populations in configurations of two interconnected chemostats. Math. Biosci. 148:1998;43.
-
(1998)
Math. Biosci.
, vol.148
, pp. 43
-
-
Lenas, P.1
Thomopoulos, N.A.2
Vayenas, D.V.3
Pavlou, S.4
-
29
-
-
0010506287
-
Competition in the gradostat: The role of the communication rate
-
Smith H., Tang B. Competition in the gradostat: The role of the communication rate. J. Math. Biol. 27:1989;139.
-
(1989)
J. Math. Biol.
, vol.27
, pp. 139
-
-
Smith, H.1
Tang, B.2
-
30
-
-
51249178956
-
The gradostat: A model of competition along a nutrient gradient
-
Smith H.L., Waltman P. The gradostat: A model of competition along a nutrient gradient. Microb. Ecol. 22:1991;207.
-
(1991)
Microb. Ecol.
, vol.22
, pp. 207
-
-
Smith, H.L.1
Waltman, P.2
-
31
-
-
0000883166
-
Effect of spatial inhomogeneities on the coexistence of competing microbial populations
-
Stephanopoulos G., Fredrickson A.G. Effect of spatial inhomogeneities on the coexistence of competing microbial populations. Biotechnol. Bioeng. 21:1979;1491.
-
(1979)
Biotechnol. Bioeng.
, vol.21
, pp. 1491
-
-
Stephanopoulos, G.1
Fredrickson, A.G.2
-
32
-
-
0010428950
-
Equilibrium distribution of species among vessels of a gradostat. A singular perturbation approach
-
Smith H.L. Equilibrium distribution of species among vessels of a gradostat. A singular perturbation approach. J. Math. Biol. 30:1991;31.
-
(1991)
J. Math. Biol.
, vol.30
, pp. 31
-
-
Smith, H.L.1
-
34
-
-
13844319644
-
The theory of the chemostat
-
Cambridge University, Cambridge
-
H.L. Smith, P. Waltman, The Theory of the Chemostat. Dynamics of Microbial Competition, Cambridge Studies in Mathematical Biology, Cambridge University, Cambridge, 1995.
-
(1995)
Dynamics of Microbial Competition, Cambridge Studies in Mathematical Biology
-
-
Smith, H.L.1
Waltman, P.2
-
35
-
-
0027329492
-
Exploitative competition in the chemostat for two perfectly substitutable resources
-
Ballyk M.M., Wolkowicz G.S.K. Exploitative competition in the chemostat for two perfectly substitutable resources. Math. Biosci. 118:1993;127.
-
(1993)
Math. Biosci.
, vol.118
, pp. 127
-
-
Ballyk, M.M.1
Wolkowicz, G.S.K.2
-
36
-
-
0023306057
-
Exploitative competition in a chemostat for two complementary, and possibly inhibitory, resources
-
Butler G.J., Wolkowicz G.S.K. Exploitative competition in a chemostat for two complementary, and possibly inhibitory, resources. Math. Biosci. 83:1987;1.
-
(1987)
Math. Biosci.
, vol.83
, pp. 1
-
-
Butler, G.J.1
Wolkowicz, G.S.K.2
-
37
-
-
0017847682
-
Two-(carbon)-substrate continuous cultures: Multiple steady states and their stability
-
Gondo S., Kaushik K., Venkatasubramanian K. Two-(carbon)-substrate continuous cultures: multiple steady states and their stability. Biotechnol. Bioeng. 20:1978;1479.
-
(1978)
Biotechnol. Bioeng.
, vol.20
, pp. 1479
-
-
Gondo, S.1
Kaushik, K.2
Venkatasubramanian, K.3
-
38
-
-
0019958718
-
Mathematical description of competition between two and three bacterial species under dual substrate limitation in the chemostat: A comparison with experimental data
-
Gottschal J.C., Thingstad T.F. Mathematical description of competition between two and three bacterial species under dual substrate limitation in the chemostat: A comparison with experimental data. Biotechnol. Bioeng. 24:1982;1403.
-
(1982)
Biotechnol. Bioeng.
, vol.24
, pp. 1403
-
-
Gottschal, J.C.1
Thingstad, T.F.2
-
39
-
-
0001010543
-
Exploitative competition of microorganisms for two complementary nutrients in continuous cultures
-
Hsu S.B., Cheng K.S., Hubbell S.P. Exploitative competition of microorganisms for two complementary nutrients in continuous cultures. SIAM J. Appl. Math. 41:1981;422.
-
(1981)
SIAM J. Appl. Math.
, vol.41
, pp. 422
-
-
Hsu, S.B.1
Cheng, K.S.2
Hubbell, S.P.3
-
40
-
-
0016718782
-
Competition between two species for two complementary or substitutable resources
-
Léon J.A., Tumpson D.B. Competition between two species for two complementary or substitutable resources. J. Theor. Biol. 50:1975;185.
-
(1975)
J. Theor. Biol.
, vol.50
, pp. 185
-
-
Léon, J.A.1
Tumpson, D.B.2
-
41
-
-
0016632639
-
Theoretical studies on the coexistence of competing species under continuous-flow conditions
-
Taylor P.A., Williams P.J.L. Theoretical studies on the coexistence of competing species under continuous-flow conditions. Can. J. Microbiol. 21:1975;90.
-
(1975)
Can. J. Microbiol.
, vol.21
, pp. 90
-
-
Taylor, P.A.1
Williams, P.J.L.2
-
42
-
-
0017400302
-
Competition for mixed substrates by microbial populations
-
Yoon H., Klinzing G., Blanch H.W. Competition for mixed substrates by microbial populations. Biotechnol. Bioeng. 19:1977;1193.
-
(1977)
Biotechnol. Bioeng.
, vol.19
, pp. 1193
-
-
Yoon, H.1
Klinzing, G.2
Blanch, H.W.3
-
43
-
-
0028990855
-
Coexistence of three competing microbial populations in a chemostat with periodically varying dilution rate
-
Lenas P., Pavlou S. Coexistence of three competing microbial populations in a chemostat with periodically varying dilution rate. Math. Biosci. 129:1995;111.
-
(1995)
Math. Biosci.
, vol.129
, pp. 111
-
-
Lenas, P.1
Pavlou, S.2
-
44
-
-
26744432460
-
Some aspects of competitive coexistence and persistence
-
in: S. Busenberg, M. Martelli (Eds.), Springer, Berlin
-
W. Jäger, H. Smith, B. Tang, Some aspects of competitive coexistence and persistence, in: S. Busenberg, M. Martelli (Eds.), Delay Differential Equations and Dynamical Systems, Springer, Berlin, 1991, p. 200.
-
(1991)
Delay Differential Equations and Dynamical Systems
, pp. 200
-
-
Jäger, W.1
Smith, H.2
Tang, B.3
-
45
-
-
0010427768
-
Competition in the gradostat for the case of three vessels and three populations
-
El-Owaidy H., Ammar A.A., El-Leithy O.A. Competition in the gradostat for the case of three vessels and three populations. Tamkang J. Math. 21:1990;143.
-
(1990)
Tamkang J. Math.
, vol.21
, pp. 143
-
-
El-Owaidy, H.1
Ammar, A.A.2
El-Leithy, O.A.3
-
46
-
-
84996102052
-
Impossibility of coexistence of three pure and simple competitors in configurations of three interconnected chemostats
-
Chang S.W., Baltzis B.C. Impossibility of coexistence of three pure and simple competitors in configurations of three interconnected chemostats. Biotechnol. Bioeng. 33:1989;460.
-
(1989)
Biotechnol. Bioeng.
, vol.33
, pp. 460
-
-
Chang, S.W.1
Baltzis, B.C.2
-
47
-
-
0027973371
-
Steady-state coexistence of three pure and simple competitors in a four-membered reactor network
-
Baltzis B.C., Wu M. Steady-state coexistence of three pure and simple competitors in a four-membered reactor network. Math. Biosci. 123:1994;147.
-
(1994)
Math. Biosci.
, vol.123
, pp. 147
-
-
Baltzis, B.C.1
Wu, M.2
-
48
-
-
38249011654
-
Asymptotic behaviour of solutions of competition in gradostat with two limiting complementary substrates
-
Zaghrout A.A.S. Asymptotic behaviour of solutions of competition in gradostat with two limiting complementary substrates. Appl. Math. and Comp. 49:1992;19.
-
(1992)
Appl. Math. and Comp.
, vol.49
, pp. 19
-
-
Zaghrout, A.A.S.1
-
49
-
-
0003487030
-
-
Center for Research on Parallel Computing, California Institute of Technology, Pasadena
-
E.J. Doedel, A.R. Champneys, T.F. Fairgrieve, Y.A. Kuznetsov, B. Sandstede and X. Wang, AUTO 97: Continuation and Bifurcation Software for Ordinary Differential Equations, User's Manual, Center for Research on Parallel Computing, California Institute of Technology, Pasadena, 1997.
-
(1997)
AUTO 97: Continuation and Bifurcation Software for Ordinary Differential Equations, User's Manual
-
-
Doedel, E.J.1
Champneys, A.R.2
Fairgrieve, T.F.3
Kuznetsov, Y.A.4
Sandstede, B.5
Wang, X.6
-
50
-
-
0032854818
-
Computing operating diagrams of bioreactors
-
in press
-
S. Pavlou, Computing operating diagrams of bioreactors. J. Biotechnol. (in press).
-
J. Biotechnol.
-
-
Pavlou, S.1
|