-
1
-
-
0005799132
-
"Stability and Hopf bifurcations in some nutrient-species models with nutrient recycling and time lags"
-
in (ed. J. C. Baltzer), (Scientific Publishing Co., IMACS, Basel)
-
E. Beretta and G. I. Bischi, "Stability and Hopf bifurcations in some nutrient-species models with nutrient recycling and time lags", in Biomedical Modelling and Simulation (ed. J. C. Baltzer), (Scientific Publishing Co., IMACS, Basel, 1989) 175-181.
-
(1989)
Biomedical Modelling and Simulation
, pp. 175-181
-
-
Beretta, E.1
Bischi, G.I.2
-
2
-
-
0025152436
-
"Stability in a chemostat model with delayed nutrient recycling"
-
E. Beretta, G. I. Bischi and F. Solimano, "Stability in a chemostat model with delayed nutrient recycling", J. Math. Biol. 28 (1990) 99-111.
-
(1990)
J. Math. Biol.
, vol.28
, pp. 99-111
-
-
Beretta, E.1
Bischi, G.I.2
Solimano, F.3
-
3
-
-
0030589781
-
"Convergence results in a well known delayed predator-prey system"
-
E. Beretta and Y. Kuang, "Convergence results in a well known delayed predator-prey system", J. Math. Anal. Appl. 204 (1996) 840-853.
-
(1996)
J. Math. Anal. Appl.
, vol.204
, pp. 840-853
-
-
Beretta, E.1
Kuang, Y.2
-
4
-
-
4243172002
-
"Global stability in a well known delayed chemostat model"
-
E. Beretta and Y. Kuang, "Global stability in a well known delayed chemostat model", Commun. Appl. Anal. 4 (2000) 147-165.
-
(2000)
Commun. Appl. Anal.
, vol.4
, pp. 147-165
-
-
Beretta, E.1
Kuang, Y.2
-
5
-
-
0011678840
-
"Global stability for chemostat equations with delayed nutrient recycling"
-
E. Beretta and Y. Takeuchi, "Global stability for chemostat equations with delayed nutrient recycling", Nonlin. World 1 (1994) 291-306.
-
(1994)
Nonlin. World
, vol.1
, pp. 291-306
-
-
Beretta, E.1
Takeuchi, Y.2
-
6
-
-
0001864149
-
"Qualitative properties of chemostat equations with time delays: Boundedness, local and global stability"
-
E. Beretta and Y. Takeuchi, "Qualitative properties of chemostat equations with time delays: boundedness, local and global stability", Differential Equations Dyn. Syst. 2 (1994) 19-40.
-
(1994)
Differential Equations Dyn. Syst.
, vol.2
, pp. 19-40
-
-
Beretta, E.1
Takeuchi, Y.2
-
7
-
-
0000128494
-
"Qualitative properties of chemostat equations with time delays II"
-
E. Beretta and Y. Takeuchi, "Qualitative properties of chemostat equations with time delays II", Differential Equations Dyn. Syst. 2 (1994) 263-288.
-
(1994)
Differential Equations Dyn. Syst.
, vol.2
, pp. 263-288
-
-
Beretta, E.1
Takeuchi, Y.2
-
9
-
-
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) 188-192.
-
(1969)
Ecology
, vol.50
, pp. 188-192
-
-
Caperon, J.1
-
10
-
-
0028419954
-
"Competition in the chemostat: Global asymptotic behaviour of a model with delayed response in growth"
-
S. P. Ellermeyer, "Competition in the chemostat: Global asymptotic behaviour of a model with delayed response in growth", SIAM J. Appl. Math. 54 (1994) 456-465.
-
(1994)
SIAM J. Appl. Math.
, vol.54
, pp. 456-465
-
-
Ellermeyer, S.P.1
-
11
-
-
0003375471
-
"Three species food chain models with mutual interference and time delays"
-
L. H. Erbe, H. I. Freedman and V. Sree Hari Rao, "Three species food chain models with mutual interference and time delays", Math. BioSciences 80 (1986) 57-80.
-
(1986)
Math. BioSciences
, vol.80
, pp. 57-80
-
-
Erbe, L.H.1
Freedman, H.I.2
Sree Hari Rao, V.3
-
12
-
-
4243131070
-
"On the dynamics of a chemostat model with delayed nutrient recycling"
-
P. Fergola, L. Jiang and Z. Ma, "On the dynamics of a chemostat model with delayed nutrient recycling", Int. J. Appl. Math. Comp. Sci. 10 (2000) 81-96.
-
(2000)
Int. J. Appl. Math. Comp. Sci.
, vol.10
, pp. 81-96
-
-
Fergola, P.1
Jiang, L.2
Ma, Z.3
-
13
-
-
0001352326
-
"Trade-off between mutual interference and time lags in predator-prey systems"
-
H. I. Freedman and V. Sree Hari Rao, "Trade-off between mutual interference and time lags in predator-prey systems", Bull. Math. Biol. 45 (1983) 991-1004.
-
(1983)
Bull. Math. Biol.
, vol.45
, pp. 991-1004
-
-
Freedman, H.I.1
Sree Hari Rao, V.2
-
14
-
-
0022768009
-
"Stability criteria for a system involving two time delays"
-
H. I. Freedman and V. Sree Hari Rao, "Stability criteria for a system involving two time delays", SIAM J. Appl. Math. 46 (1986) 552-560.
-
(1986)
SIAM J. Appl. Math.
, vol.46
, pp. 552-560
-
-
Freedman, H.I.1
Sree Hari Rao, V.2
-
15
-
-
4243155784
-
"Stability, persistence and extinction in a predator-prey system with discrete and continuous time delays"
-
H. I. Freedman, V. Sree Hari Rao and K. J. Lakshmi, "Stability, persistence and extinction in a predator-prey system with discrete and continuous time delays", WSSIAA 1 (1992) 221-238.
-
(1992)
WSSIAA
, vol.1
, pp. 221-238
-
-
Freedman, H.I.1
Sree Hari Rao, V.2
Lakshmi, K.J.3
-
16
-
-
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) 859-870.
-
(1989)
SIAM J. Appl. Math.
, vol.49
, pp. 859-870
-
-
Freedman, H.I.1
So, J.W.H.2
Waltman, P.3
-
17
-
-
0001759394
-
"Competing predators for a prey in a chemostat model with periodic nutrient input"
-
H. I. Freedman and F. Yang, "Competing predators for a prey in a chemostat model with periodic nutrient input", J. Math. Biol. 29 (1991) 715-732.
-
(1991)
J. Math. Biol.
, vol.29
, pp. 715-732
-
-
Freedman, H.I.1
Yang, F.2
-
18
-
-
0002797068
-
"Model of competition in the chemostat with instantaneous and delayed nutrient recycling"
-
H. I. Freedman and Y. Xu, "Model of competition in the chemostat with instantaneous and delayed nutrient recycling", J. Math. Biol. 31 (1993) 513-527.
-
(1993)
J. Math. Biol.
, vol.31
, pp. 513-527
-
-
Freedman, H.I.1
Xu, Y.2
-
19
-
-
0006674647
-
"Global stability in chemostat-type plankton models with delayed nutrient recycling"
-
X.-Z. He and S. Ruan, "Global stability in chemostat-type plankton models with delayed nutrient recycling", J. Math. Biol. 37 (1998) 253-271.
-
(1998)
J. Math. Biol.
, vol.37
, pp. 253-271
-
-
He, X.-Z.1
Ruan, S.2
-
20
-
-
0032399698
-
"Global stability in chemostat-type equations with distributed delays"
-
X.-Z. He, S. Ruan and H. Xia, "Global stability in chemostat-type equations with distributed delays", SIAM J. Math. Anal. 29 (1998) 681-696.
-
(1998)
SIAM J. Math. Anal.
, vol.29
, pp. 681-696
-
-
He, X.-Z.1
Ruan, S.2
Xia, H.3
-
23
-
-
4243189861
-
"Global stability of chemostat models involving time delays and zones of no activation"
-
V. Sree Hari Rao and P. Raja Sekhara Rao, "Global stability of chemostat models involving time delays and zones of no activation", Canad. Appl. Math. Quart. 9 (2001) 273-300.
-
(2001)
Canad. Appl. Math. Quart.
, vol.9
, pp. 273-300
-
-
Sree Hari Rao, V.1
Raja Sekhara Rao, P.2
-
24
-
-
0041573457
-
"Global stability of chemostat models involving time delays and wall growth"
-
V. Sree Hari Rao and P. Raja Sekhara Rao, "Global stability of chemostat models involving time delays and wall growth", Nonlinear Anal. Real World Appl. 5 (2004) 141-158.
-
(2004)
Nonlinear Anal. Real World Appl.
, vol.5
, pp. 141-158
-
-
Sree Hari Rao, V.1
Raja Sekhara Rao, P.2
-
25
-
-
4243085710
-
"Mathematical models of microbial populations and issues concerning stability"
-
V. Sree Hari Rao and P. Raja Sekhara Rao, "Mathematical models of microbial populations and issues concerning stability", Chaos Solitons Fractals 23 (2005) 657-670.
-
(2005)
Chaos Solitons Fractals
, vol.23
, pp. 657-670
-
-
Sree Hari Rao, V.1
Raja Sekhara Rao, P.2
-
26
-
-
13544275551
-
"Oscillations induced by time lags in limited nutrient-consumer dynamic models"
-
V. Sree Hari Rao and P. Raja Sekhara Rao, "Oscillations induced by time lags in limited nutrient-consumer dynamic models", Chaos Solitons Fractals 25 (2005) 11-23.
-
(2005)
Chaos Solitons Fractals
, vol.25
, pp. 11-23
-
-
Sree Hari Rao, V.1
Raja Sekhara Rao, P.2
-
27
-
-
85126433994
-
"Mathematical models and stabilizing bio-control mechanisms for microbial populations in a cultured environment"
-
(in press)
-
V. Sree Hari Rao and P. Raja Sekhara Rao, "Mathematical models and stabilizing bio-control mechanisms for microbial populations in a cultured environment", Chaos Solitons Fractals (in press).
-
Chaos Solitons Fractals
-
-
Sree Hari Rao, V.1
Raja Sekhara Rao, P.2
-
28
-
-
28244448601
-
"Parameter estimation using dynamic optimization in limited nutrient-consumer hybrid dynamical systems"
-
V. Sree Hari Rao, P. Raja Sekhara Rao and K. Venkata Ratnam, "Parameter estimation using dynamic optimization in limited nutrient-consumer hybrid dynamical systems", Special issue on Hybrid Dynamical Systems, Nonlinear Anal. 64 (2006) 263-287.
-
(2006)
Special Issue on Hybrid Dynamical Systems, Nonlinear Anal.
, vol.64
, pp. 263-287
-
-
Sree Hari Rao, V.1
Raja Sekhara Rao, P.2
Venkata Ratnam, K.3
-
29
-
-
0000778770
-
"The effect of delays on stability and persistence in plankton models"
-
S. Ruan, "The effect of delays on stability and persistence in plankton models", Nonlinear Anal. 24 (1995) 575-585.
-
(1995)
Nonlinear Anal.
, vol.24
, pp. 575-585
-
-
Ruan, S.1
-
30
-
-
0031997297
-
"Global stability in chemostat-type competition models with nutrient recycling"
-
S. Ruan and X.-Z. He, "Global stability in chemostat-type competition models with nutrient recycling", SIAM J. Appl. Math. 58 (1998) 170-192.
-
(1998)
SIAM J. Appl. Math.
, vol.58
, pp. 170-192
-
-
Ruan, S.1
He, X.-Z.2
-
32
-
-
3042525371
-
"Coexistence in chemostat-like models"
-
P. Waltman, "Coexistence in chemostat-like models", Rocky Mountain J. Math. 20 (1990) 777-807.
-
(1990)
Rocky Mountain J. Math.
, vol.20
, pp. 777-807
-
-
Waltman, P.1
-
33
-
-
0031258276
-
"Competition in the chemostat: A distributed delay model and its global asymptotic behaviour"
-
G. S. K. Wolkowicz, H. Xia and S. Ruan, "Competition in the chemostat: a distributed delay model and its global asymptotic behaviour", SIAM J. Appl. Math. 55 (1997) 1281-13 10.
-
(1997)
SIAM J. Appl. Math.
, vol.55
, pp. 1281-1310
-
-
Wolkowicz, G.S.K.1
Xia, H.2
Ruan, S.3
-
34
-
-
1642312070
-
"Direction and stability of bifurcating periodic solutions of a chemostat model with two distributed delays"
-
S. Yuan, M. Song and M. Han, "Direction and stability of bifurcating periodic solutions of a chemostat model with two distributed delays", Chaos Solitons Fractals 21 (2004) 1109-1123.
-
(2004)
Chaos Solitons Fractals
, vol.21
, pp. 1109-1123
-
-
Yuan, S.1
Song, M.2
Han, M.3
|