-
1
-
-
0001188059
-
Competitive exclusion
-
R. A. ARMSTRONG AND R. MCGEHEE, Competitive exclusion, Amer. Natur., 115 (1980), pp. 151-170.
-
(1980)
Amer. Natur.
, vol.115
, pp. 151-170
-
-
Armstrong, R.A.1
Mcgehee, R.2
-
2
-
-
0017173061
-
The effect of time delay and growth rate inhibition in the bacterial treatment of wastewater
-
A. W. BUSH AND A. E. COOK, The effect of time delay and growth rate inhibition in the bacterial treatment of wastewater, J. Theor. Biol., 63 (1976), pp. 385-395.
-
(1976)
J. Theor. Biol.
, vol.63
, pp. 385-395
-
-
Bush, A.W.1
Cook, A.E.2
-
3
-
-
0022012911
-
A mathematical model of the chemostat with a general class of functions describing nutrient uptake
-
G. J. BUTLER AND G. S. K. WOLKOWICZ, A mathematical model of the chemostat with a general class of functions describing nutrient uptake, SIAM J. Appl. Math., 45 (1985), pp. 138-151.
-
(1985)
SIAM J. Appl. Math.
, vol.45
, pp. 138-151
-
-
Butler, G.J.1
Wolkowicz, G.S.K.2
-
4
-
-
0001453657
-
Time lag in population growth response of Isochrysis galbana to a variable nitrate environment
-
J. CAPERON, Time lag in population growth response of Isochrysis galbana to a variable nitrate environment, Ecology, 50 (1969), pp. 188-192.
-
(1969)
Ecology
, vol.50
, pp. 188-192
-
-
Caperon, J.1
-
5
-
-
0017889955
-
Time lag and nutrient storage effects in the transient growth response of Chlamydomonas reinhardii in nitrogen-limited batch and continuous culture
-
A. CUNNINGHAM AND P. MAAS, Time lag and nutrient storage effects in the transient growth response of Chlamydomonas reinhardii in nitrogen-limited batch and continuous culture, J. Gen. Microbiol., 104 (1978), pp. 227-231.
-
(1978)
J. Gen. Microbiol.
, vol.104
, pp. 227-231
-
-
Cunningham, A.1
Maas, P.2
-
6
-
-
0018839365
-
Time lag and co-operativity in the transient growth dynamics of microalgae
-
A. CUNNINGHAM AND R. M. NISBET, Time lag and co-operativity in the transient growth dynamics of microalgae, J. Theor. Biol., 84 (1980), pp. 189-203.
-
(1980)
J. Theor. Biol.
, vol.84
, pp. 189-203
-
-
Cunningham, A.1
Nisbet, R.M.2
-
7
-
-
84974142363
-
12 and marine ecology. IV. the kinetics of uptake, growth, and inhibition in Monochrysis lutheri
-
12 and marine ecology. IV. The kinetics of uptake, growth, and inhibition in Monochrysis lutheri, J. Mar. Biol. Assoc. UK, 48 (1968), pp. 689-733.
-
(1968)
J. Mar. Biol. Assoc. UK
, vol.48
, pp. 689-733
-
-
Droop, M.R.1
-
8
-
-
0028419954
-
Competition in the chemostat: Global asymptotic behavior of a model with delayed response in growth
-
S. F. ELLERMEYER, Competition in the chemostat: Global asymptotic behavior of a model with delayed response in growth, SIAM J. Appl. Math., 54 (1994), pp. 456-465.
-
(1994)
SIAM J. Appl. Math.
, vol.54
, pp. 456-465
-
-
Ellermeyer, S.F.1
-
10
-
-
0003068294
-
Population dynamics of a continuous propagator for microorganisms
-
R. K. FINN AND R. E. WILSON, Population dynamics of a continuous propagator for microorganisms, J. Agric. Food Chem., 2 (1953), pp. 66-69.
-
(1953)
J. Agric. Food Chem.
, vol.2
, pp. 66-69
-
-
Finn, R.K.1
Wilson, R.E.2
-
11
-
-
0001503284
-
Coexistence in a model of competition in the chemostat incorporating discrete delays
-
H. I. FREEDMAN, J. W.-H. SO, AND P. WALTMAN, Coexistence in a model of competition in the chemostat incorporating discrete delays, SIAM J. Appl. Math., 49 (1989), pp. 859-870.
-
(1989)
SIAM J. Appl. Math.
, vol.49
, pp. 859-870
-
-
Freedman, H.I.1
So, J.W.-H.2
Waltman, P.3
-
12
-
-
0343749071
-
Chemostat competition with time delays
-
J. Eisenfeld and D. S. Levine, eds., Baltzer Scientific Publishing, Basel
-
H. I. FREEDMAN, J. W.-H. SO, AND P. WALTMAN, Chemostat competition with time delays, in Biomedical Modelling and Simulation, J. Eisenfeld and D. S. Levine, eds., Baltzer Scientific Publishing, Basel, 1989, pp. 171-173.
-
(1989)
Biomedical Modelling and Simulation
, pp. 171-173
-
-
Freedman, H.I.1
So, J.W.-H.2
Waltman, P.3
-
14
-
-
0003257944
-
Life table data and population dynamics of the rotifer Brachionus Calyciflorus pallas as influenced by periodically oscillating temperature
-
W. Wieser, ed., Springer-Verlag, Heidelberg
-
U. HALBACH, Life table data and population dynamics of the rotifer Brachionus Calyciflorus pallas as influenced by periodically oscillating temperature, in Effects of Temperature on Ectothermic Organisms, W. Wieser, ed., Springer-Verlag, Heidelberg, 1973, pp. 217-228.
-
(1973)
Effects of Temperature on Ectothermic Organisms
, pp. 217-228
-
-
Halbach, U.1
-
15
-
-
0018868854
-
Single-nutrient microbial competition: Qualitative agreement between experimental and theoretically forecast outcomes
-
S. R. HANSEN AND S. P. HUBBELL, Single-nutrient microbial competition: qualitative agreement between experimental and theoretically forecast outcomes, Science, 207 (1980), pp. 1491-1493.
-
(1980)
Science
, vol.207
, pp. 1491-1493
-
-
Hansen, S.R.1
Hubbell, S.P.2
-
16
-
-
0002698568
-
Low temperature adaptation in bacteria
-
G. J. Morris and A. Clarke, eds., Academic Press, London
-
R. A. HERBERT, Low temperature adaptation in bacteria, in Effects of Low Temperature on Biological Membranes, G. J. Morris and A. Clarke, eds., Academic Press, London, 1981, pp. 41-53.
-
(1981)
Effects of Low Temperature on Biological Membranes
, pp. 41-53
-
-
Herbert, R.A.1
-
17
-
-
84968480336
-
The dynamical systems approach to differential equations
-
M. W. HIRSCH, The dynamical systems approach to differential equations, Bull. Amer. Math. Soc., 11 (1984), pp. 1-64.
-
(1984)
Bull. Amer. Math. Soc.
, vol.11
, pp. 1-64
-
-
Hirsch, M.W.1
-
18
-
-
84990581010
-
Differential equation models of some parasitic infections: Methods for the study of asymptotic behavior
-
W. M. HIRSCH, H. HANISCH, AND J.-P. GABRIEL, Differential equation models of some parasitic infections: methods for the study of asymptotic behavior, Comm. Pure Appl. Math., 38 (1985), pp. 733-753.
-
(1985)
Comm. Pure Appl. Math.
, vol.38
, pp. 733-753
-
-
Hirsch, W.M.1
Hanisch, H.2
Gabriel, J.-P.3
-
19
-
-
0000468175
-
Limiting behavior for competing species
-
S. B. HSU, Limiting behavior for competing species, SIAM J. Appl. Math., 34 (1978), pp. 760-763.
-
(1978)
SIAM J. Appl. Math.
, vol.34
, pp. 760-763
-
-
Hsu, S.B.1
-
20
-
-
0000875842
-
A mathematical theory for single-nutrient competition in continuous cultures of micro-organisms
-
S. B. HSU, S. HUBBELL, AND P. WALTMAN, A mathematical theory for single-nutrient competition in continuous cultures of micro-organisms, SIAM J. Appl. Math., 32 (1977), pp. 366-383.
-
(1977)
SIAM J. Appl. Math.
, vol.32
, pp. 366-383
-
-
Hsu, S.B.1
Hubbell, S.2
Waltman, P.3
-
21
-
-
84972528293
-
A remark on the global asymptotic stability of a dynamical system modeling two species competition
-
S. B. HSU, P. WALTMAN, AND S. F. ELLERMEYER, A remark on the global asymptotic stability of a dynamical system modeling two species competition, Hiroshima Math. J., 24 (1994), pp. 435-445.
-
(1994)
Hiroshima Math. J.
, vol.24
, pp. 435-445
-
-
Hsu, S.B.1
Waltman, P.2
Ellermeyer, S.F.3
-
22
-
-
0242462332
-
Experimental bacterial ecology studied in continuous culture
-
A. H. Rose and D. W. Tempest, eds., Academic Press, London
-
H. W. JANNASCH AND R. I. MATELES, Experimental bacterial ecology studied in continuous culture, in Advances in Microbial Physiology, Vol. 11, A. H. Rose and D. W. Tempest, eds., Academic Press, London, 1974, pp. 165-212.
-
(1974)
Advances in Microbial Physiology
, vol.11
, pp. 165-212
-
-
Jannasch, H.W.1
Mateles, R.I.2
-
24
-
-
0026671814
-
The attractiveness of the Droop equations
-
K. LANGE AND F. J. OYARZUN, The attractiveness of the Droop equations, Math. Biosci., 111 (1992), pp. 261-278.
-
(1992)
Math. Biosci.
, vol.111
, pp. 261-278
-
-
Lange, K.1
Oyarzun, F.J.2
-
25
-
-
0017126376
-
Time delay in simple chemostat models
-
N. MACDONALD, Time delay in simple chemostat models, Biotechnol. and Bioeng., 18 (1976), pp. 805-812.
-
(1976)
Biotechnol. and Bioeng.
, vol.18
, pp. 805-812
-
-
Macdonald, N.1
-
26
-
-
0003289006
-
Time Lags in Biological Models
-
Springer-Verlag, Berlin
-
N. MACDONALD, Time Lags in Biological Models, Lecture Notes in Biomath. 27, Springer-Verlag, Berlin, 1978.
-
(1978)
Lecture Notes in Biomath.
, vol.27
-
-
Macdonald, N.1
-
27
-
-
0002477803
-
Time delays in chemostat models
-
M. J. Bazin, ed., CRC Press, Boca Raton, FL
-
N. MACDONALD, Time delays in chemostat models, in Microbial Population Dynamics, M. J. Bazin, ed., CRC Press, Boca Raton, FL, 1982.
-
(1982)
Microbial Population Dynamics
-
-
Macdonald, N.1
-
28
-
-
0000703838
-
Asymptotically autonomous semiflows: Chain recurrence and Lyapunov functions
-
K. MISCHAIKOW, H. L. SMITH, AND H. R. THIEME, Asymptotically autonomous semiflows: chain recurrence and Lyapunov functions, Trans. Amer. Math. Soc., 347 (1995), pp. 1669-1685.
-
(1995)
Trans. Amer. Math. Soc.
, vol.347
, pp. 1669-1685
-
-
Mischaikow, K.1
Smith, H.L.2
Thieme, H.R.3
-
29
-
-
0000369563
-
La technique de culture continue; théorie et applications
-
J. MONOD, La technique de culture continue; théorie et applications, Ann. Inst. Pasteur, 79 (1950), pp. 390-401.
-
(1950)
Ann. Inst. Pasteur
, vol.79
, pp. 390-401
-
-
Monod, J.1
-
31
-
-
0028363349
-
The attractiveness of the Droop equations II. Generic uptake and growth functions
-
F. J. OYARZUN AND K. LANGE, The attractiveness of the Droop equations II. Generic uptake and growth functions, Math. Biosci., 121 (1994), pp. 127-139.
-
(1994)
Math. Biosci.
, vol.121
, pp. 127-139
-
-
Oyarzun, F.J.1
Lange, K.2
-
32
-
-
0002844130
-
The growth rate of microorganisms as a function of substrate concentration
-
E. O. Powell, C. G. T. Evans, R. E. Strange, and D. W. Tempest, eds. Her Majesty's Stationery Office, London
-
E. O. POWELL, The growth rate of microorganisms as a function of substrate concentration, in Continuous Cultivation of Microorganisms, E. O. Powell, C. G. T. Evans, R. E. Strange, and D. W. Tempest, eds. Her Majesty's Stationery Office, London, 1967, pp. 34-55.
-
(1967)
Continuous Cultivation of Microorganisms
, pp. 34-55
-
-
Powell, E.O.1
-
33
-
-
0030589755
-
Bifurcation analysis of a chemostat model with a distributed delay
-
S. RUAN AND G. S. K. WOLKOWICZ, Bifurcation analysis of a chemostat model with a distributed delay, J. Math. Anal. Appl., 204 (1996), pp. 786-812.
-
(1996)
J. Math. Anal. Appl.
, vol.204
, pp. 786-812
-
-
Ruan, S.1
Wolkowicz, G.S.K.2
-
34
-
-
0001243427
-
Monotone semiflows generated by functional differential equations
-
H. SMITH, Monotone semiflows generated by functional differential equations, J. Differential Equations, 66 (1987), pp. 420-442.
-
(1987)
J. Differential Equations
, vol.66
, pp. 420-442
-
-
Smith, H.1
-
35
-
-
0001676484
-
Strongly order preserving semi-flows generated by functional differential equations
-
H. SMITH AND H. R. THIEME, Strongly order preserving semi-flows generated by functional differential equations, J. Differential Equations, 93 (1991), pp. 332-363.
-
(1991)
J. Differential Equations
, vol.93
, pp. 332-363
-
-
Smith, H.1
Thieme, H.R.2
-
36
-
-
0028483826
-
Competition for a single limiting resource in continuous culture: The variable-yield model
-
H. SMITH AND P. WALTMAN, Competition for a single limiting resource in continuous culture: the variable-yield model, SIAM J. Appl. Math., 54 (1994), pp. 1113-1131.
-
(1994)
SIAM J. Appl. Math.
, vol.54
, pp. 1113-1131
-
-
Smith, H.1
Waltman, P.2
-
38
-
-
0023327936
-
Effect of cycling on final mixed culture fate
-
M. L. STEPHENS AND G. LYBERATOS, Effect of cycling on final mixed culture fate, Biotechnol. Bioeng., 29 (1987), pp. 672-678.
-
(1987)
Biotechnol. Bioeng.
, vol.29
, pp. 672-678
-
-
Stephens, M.L.1
Lyberatos, G.2
-
39
-
-
77952672921
-
Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations
-
H. R. THIEME, Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations, J. Math. Biol., 30 (1992), pp. 755-763.
-
(1992)
J. Math. Biol.
, vol.30
, pp. 755-763
-
-
Thieme, H.R.1
-
40
-
-
0016299795
-
Dynamics of chemostat culture: The effect of a delay in cell response
-
T. F. THINGSTAD AND T. I. LANGELAND, Dynamics of chemostat culture: The effect of a delay in cell response, J. Theor. Biol., 48 (1974), pp. 149-159.
-
(1974)
J. Theor. Biol.
, vol.48
, pp. 149-159
-
-
Thingstad, T.F.1
Langeland, T.I.2
-
42
-
-
0002212436
-
Ecological studies with the chemostat
-
M. Alexander, ed., Plenum Press, New York
-
H. VELDKAMP, Ecological studies with the chemostat, in Advances in Microbial Ecology, Vol. 1, M. Alexander, ed., Plenum Press, New York, 1977, pp. 59-94.
-
(1977)
Advances in Microbial Ecology
, vol.1
, pp. 59-94
-
-
Veldkamp, H.1
-
44
-
-
85053514649
-
Theoretical and experimental investigations of microbial competition in continuous culture
-
T. A. Burton, ed., Marcel Dekker, New York
-
P. WALTMAN, S. P. HUBBELL, AND S. B. HSU, Theoretical and experimental investigations of microbial competition in continuous culture, in Modeling and Differential Equations in Biology, T. A. Burton, ed., Marcel Dekker, New York, 1980, pp. 107-152.
-
(1980)
Modeling and Differential Equations in Biology
, pp. 107-152
-
-
Waltman, P.1
Hubbell, S.P.2
Hsu, S.B.3
-
45
-
-
0026818163
-
Global dynamics of a mathematical model of competition in the chemostat: General response functions and differential death rates
-
G. S. K. WOLKOWICZ AND Z. LU, Global dynamics of a mathematical model of competition in the chemostat: General response functions and differential death rates, SIAM J. Appl. Math., 52 (1992), pp. 222-233.
-
(1992)
SIAM J. Appl. Math.
, vol.52
, pp. 222-233
-
-
Wolkowicz, G.S.K.1
Lu, Z.2
-
46
-
-
0011690047
-
Microbial dynamics in a chemostat: Competition, growth, implications of enrichment
-
Differential Equations and Control Theory, Z. Deng, G. Lu, and S. Ruan, eds., Marcel Dekker, New York
-
G. S. K. WOLKOWICZ, M. M. BALLYK, AND Z. Lu, Microbial dynamics in a chemostat: competition, growth, implications of enrichment, in Differential Equations and Control Theory, Lecture Notes in Pure and Appl. Math. 176, Z. Deng, G. Lu, and S. Ruan, eds., Marcel Dekker, New York, 1995, pp. 389-406.
-
(1995)
Lecture Notes in Pure and Appl. Math.
, vol.176
, pp. 389-406
-
-
Wolkowicz, G.S.K.1
Ballyk, M.M.2
Lu, Z.3
-
47
-
-
0031208159
-
Competition in the chemostat: A distributed delay model and its global asymptotic behavior
-
to appear
-
G. S. K. WOLKOWICZ, H. XIA, AND S. RUAN, Competition in the chemostat: A distributed delay model and its global asymptotic behavior, SIAM J. Appl. Math., 57 (1997), to appear.
-
(1997)
SIAM J. Appl. Math.
, vol.57
-
-
Wolkowicz, G.S.K.1
Xia, H.2
Ruan, S.3
-
48
-
-
0011560396
-
Global periodic solutions for a differential delay system modelling a microbial population in the chemostat
-
T. ZHAO, Global periodic solutions for a differential delay system modelling a microbial population in the chemostat, J. Math. Anal. Appl., 193 (1995), pp. 329-352.
-
(1995)
J. Math. Anal. Appl.
, vol.193
, pp. 329-352
-
-
Zhao, T.1
|