-
1
-
-
0033979874
-
Comparison of deterministic and stochastic SIS and SIR models in discrete-time
-
L. J. S. ALLEN AND A. M. BURGIN, Comparison of deterministic and stochastic SIS and SIR models in discrete-time, Math. Biosci., 163 (2000), pp. 1-33.
-
(2000)
Math. Biosci.
, vol.163
, pp. 1-33
-
-
Allen, L.J.S.1
Burgin, A.M.2
-
2
-
-
0028116676
-
Some discrete-time SI, SIR and SIS epidemic models
-
L. J. S. ALLEN, Some discrete-time SI, SIR and SIS epidemic models, Math. Biosci., 124 (1994), pp. 83-105.
-
(1994)
Math. Biosci.
, vol.124
, pp. 83-105
-
-
Allen, L.J.S.1
-
5
-
-
0003408552
-
-
Blackwell Science, Williston, VT
-
M. BEGON, J. L. HARPER, AND C. R. TOWNSEND, Ecology: Individuals, Populations and Communities, Blackwell Science, Williston, VT, 1996.
-
(1996)
Ecology: Individuals, Populations and Communities
-
-
Begon, M.1
Harper, J.L.2
Townsend, C.R.3
-
6
-
-
0003531546
-
On the dynamics of exploited fish populations
-
H. M. Stationery Office, London
-
R. J. H. BEVERTON AND S. J. HOLT, On the Dynamics of Exploited Fish Populations, Fish. Invest. Ser. II, H. M. Stationery Office, London, 1957.
-
(1957)
Fish. Invest. Ser. II
-
-
Beverton, R.J.H.1
Holt, S.J.2
-
7
-
-
0034770285
-
Dispersal, disease and life-history evolution
-
C. CASTILLO-CHAVEZ AND A. YAKUBU, Dispersal, disease and life-history evolution, Math. Biosci., 173 (2001), pp. 35-53.
-
(2001)
Math. Biosci.
, vol.173
, pp. 35-53
-
-
Castillo-Chavez, C.1
Yakubu, A.2
-
8
-
-
0035425152
-
Discrete-time S-I-S models with complex dynamics
-
C. CASTILLO-CHAVEZ AND A. YAKUBU, Discrete-time S-I-S models with complex dynamics, Nonlinear Anal., 47 (2001), pp. 4753-4762.
-
(2001)
Nonlinear Anal.
, vol.47
, pp. 4753-4762
-
-
Castillo-Chavez, C.1
Yakubu, A.2
-
9
-
-
0011058386
-
Intraspecific competition, dispersal and disease dynamics in discrete-time patchy environments
-
C. Castillo-Chavez with S. Blower, P. van den Driessche, D. Kirschner, and A.-A. Yakubu, eds., Springer-Verlag, New York
-
C. CASTILLO-CHAVEZ AND A. A. YAKUBU, Intraspecific competition, dispersal and disease dynamics in discrete-time patchy environments, in Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction to Models, Methods and Theory, C. Castillo-Chavez with S. Blower, P. van den Driessche, D. Kirschner, and A.-A. Yakubu, eds., Springer-Verlag, New York, 2002, pp. 165-181.
-
(2002)
Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction to Models, Methods and Theory
, pp. 165-181
-
-
Castillo-Chavez, C.1
Yakubu, A.A.2
-
10
-
-
0018185508
-
On the growth of populations with narrow spread in reproductive age. I. General theory and examples
-
B. D. COLEMAN, On the growth of populations with narrow spread in reproductive age. I. General theory and examples, J. Math. Biol., 6 (1978), pp. 1-19.
-
(1978)
J. Math. Biol.
, vol.6
, pp. 1-19
-
-
Coleman, B.D.1
-
11
-
-
0040699430
-
Satiable egg eating predators
-
C. S. COLEMAN AND J. C. FRAUENTHAL, Satiable egg eating predators, Math. Biosci., 63 (1983), pp. 99-119.
-
(1983)
Math. Biosci.
, vol.63
, pp. 99-119
-
-
Coleman, C.S.1
Frauenthal, J.C.2
-
12
-
-
4243091994
-
Some equations modelling growth processes of gonorrhea epidemics
-
K. L. COOKE AND J. A. YORKE, Some equations modelling growth processes of gonorrhea epidemics, Math. Biosci., 58 (1973), pp. 93-109.
-
(1973)
Math. Biosci.
, vol.58
, pp. 93-109
-
-
Cooke, K.L.1
Yorke, J.A.2
-
13
-
-
0032029704
-
Resonant population cycles in temporarily fluctuating habitats
-
R. F. COSTANTINO, J. M. CUSHING, B. DENNIS, R. A. DESHARNAIS, AND S. M. HENSON, Resonant population cycles in temporarily fluctuating habitats, Bull, Math. Biol., 60 (1998), pp. 247-273.
-
(1998)
Bull, Math. Biol.
, vol.60
, pp. 247-273
-
-
Costantino, R.F.1
Cushing, J.M.2
Dennis, B.3
Desharnais, R.A.4
Henson, S.M.5
-
14
-
-
0011829541
-
Global dynamics of some periodically forced, monotone difference equations
-
J. M. CUSHING AND S. M. HENSON, Global dynamics of some periodically forced, monotone difference equations, J. Differential Equations Appl., 7 (2001), pp. 859-872.
-
(2001)
J. Differential Equations Appl.
, vol.7
, pp. 859-872
-
-
Cushing, J.M.1
Henson, S.M.2
-
15
-
-
0003981716
-
-
Chapman & Hall/CRC, Boca Raton, FL
-
S. N. ELAYDI, Discrete Chaos, Chapman & Hall/CRC, Boca Raton, FL, 2000.
-
(2000)
Discrete Chaos
-
-
Elaydi, S.N.1
-
16
-
-
38149147243
-
Periodicity and stability of linear Volterra difference equations
-
S. N. ELAYDI, Periodicity and stability of linear Volterra difference equations, J. Math. Anal. Appl., 181 (1994), pp. 483-492.
-
(1994)
J. Math. Anal. Appl.
, vol.181
, pp. 483-492
-
-
Elaydi, S.N.1
-
17
-
-
10944258097
-
Global stability of periodic orbits of nonautonomous difference equations and population biology
-
S. N. ELAYDI AND R. J. SACKER, Global stability of periodic orbits of nonautonomous difference equations and population biology, J. Differential Equations, 208 (2005), pp. 258-273.
-
(2005)
J. Differential Equations
, vol.208
, pp. 258-273
-
-
Elaydi, S.N.1
Sacker, R.J.2
-
18
-
-
33748293070
-
Global stability of periodic orbits of nonautonomous difference equations in population biology and Gushing-Henson conjectures
-
Chapman & Hall/CRC, Boca Raton, FL
-
S. N. ELAYDI AND R. J. SACKER, Global stability of periodic orbits of nonautonomous difference equations in population biology and Gushing-Henson conjectures, in Proceedings of the 8th International Conference on Difference Equations and Applications, Chapman & Hall/CRC, Boca Raton, FL, 2005, pp. 113-126.
-
(2005)
Proceedings of the 8th International Conference on Difference Equations and Applications
, pp. 113-126
-
-
Elaydi, S.N.1
Sacker, R.J.2
-
19
-
-
22544488393
-
Nonautonomous Beverton-Holt equations and the Cushing-Henson conjectures
-
S. N. ELAYDI AND R. J. SACKER, Nonautonomous Beverton-Holt equations and the Cushing-Henson conjectures, J. Differential Equations Appl., 11 (2005), pp. 336-346.
-
(2005)
J. Differential Equations Appl.
, vol.11
, pp. 336-346
-
-
Elaydi, S.N.1
Sacker, R.J.2
-
21
-
-
0036622687
-
Global stability of cycles: Lotka-Volterra competition model with stocking
-
S. N. ELAYDI AND A.-A. YAKUBU, Global stability of cycles: Lotka-Volterra competition model with stocking, J. Differential Equations Appl., 8 (2002), pp. 537-549.
-
(2002)
J. Differential Equations Appl.
, vol.8
, pp. 537-549
-
-
Elaydi, S.N.1
Yakubu, A.-A.2
-
22
-
-
0142056112
-
Attractor for periodic dynamical systems
-
J. E. FRANKE AND J. F. SELGRADE, Attractor for periodic dynamical systems, J. Math. Anal. Appl., 286 (2003), pp. 64-79.
-
(2003)
J. Math. Anal. Appl.
, vol.286
, pp. 64-79
-
-
Franke, J.E.1
Selgrade, J.F.2
-
23
-
-
24144453072
-
Periodic dynamical systems in unidirectional metapopulation models
-
J. E. FRANKE AND A.-A. YAKUBU, Periodic dynamical systems in unidirectional metapopulation models, J. Differential Equations Appl., 11 (2005), pp. 687-700.
-
(2005)
J. Differential Equations Appl.
, vol.11
, pp. 687-700
-
-
Franke, J.E.1
Yakubu, A.-A.2
-
24
-
-
22544487784
-
Multiple attractors via cusp bifurcation in periodically varying environments
-
J. E. FRANKE AND A.-A. YAKUBU, Multiple attractors via cusp bifurcation in periodically varying environments, J. Differential Equations Appl., 11 (2005), pp. 365-377.
-
(2005)
J. Differential Equations Appl.
, vol.11
, pp. 365-377
-
-
Franke, J.E.1
Yakubu, A.-A.2
-
25
-
-
32644470436
-
Population models with periodic recruitment functions and survival rates
-
J. E. FRANKE AND A.-A. YAKUBU, Population models with periodic recruitment functions and survival rates, J. Differential Equations Appl., 11 (2005), pp. 1169-1184.
-
(2005)
J. Differential Equations Appl.
, vol.11
, pp. 1169-1184
-
-
Franke, J.E.1
Yakubu, A.-A.2
-
27
-
-
0030882301
-
Backward bifurcation in epidemic control
-
K. P. HADELER AND P. VAN DEN DRIESSCHE, Backward bifurcation in epidemic control, Math. Biosci., 146 (1997), pp. 15-35.
-
(1997)
Math. Biosci.
, vol.146
, pp. 15-35
-
-
Hadeler, K.P.1
Van Den Driessche, P.2
-
28
-
-
0003326039
-
The dynamics of competition and predation
-
The Camelot Press, Southampton, UK
-
M. P. HASSELL, The Dynamics of Competition and Predation, Studies in Biol. 72, The Camelot Press, Southampton, UK, 1976.
-
(1976)
Studies in Biol.
, vol.72
-
-
Hassell, M.P.1
-
29
-
-
0001717061
-
Patterns of dynamical behavior in single species populations
-
M. P. HASSELL, J. H. LAWTON, AND R. M. MAY, Patterns of dynamical behavior in single species populations, J. Animal Ecol., 45 (1976), pp. 471-486.
-
(1976)
J. Animal Ecol.
, vol.45
, pp. 471-486
-
-
Hassell, M.P.1
Lawton, J.H.2
May, R.M.3
-
30
-
-
0346684337
-
Multiple attractors and resonance in periodically forced population models
-
S. M. HENSON, Multiple attractors and resonance in periodically forced population models, Phys. D, 140 (2000), pp. 33-49.
-
(2000)
Phys. D
, vol.140
, pp. 33-49
-
-
Henson, S.M.1
-
31
-
-
0345844525
-
The effect of periodicity in maps
-
S. M. HENSON, The effect of periodicity in maps, J. Differential Equations Appl., 5 (1999), pp. 31-56.
-
(1999)
J. Differential Equations Appl.
, vol.5
, pp. 31-56
-
-
Henson, S.M.1
-
32
-
-
0032701814
-
Multiple attractors, saddles, and population dynamics in periodic habitats
-
S. M. HENSON, R. F. COSTANTINO, J. M. CUSHING, B. DENNIS, AND R. A. DESHARNAIS, Multiple attractors, saddles, and population dynamics in periodic habitats, Bull. Math. Biol., 61 (1999), pp. 1121-1149.
-
(1999)
Bull. Math. Biol.
, vol.61
, pp. 1121-1149
-
-
Henson, S.M.1
Costantino, R.F.2
Cushing, J.M.3
Dennis, B.4
Desharnais, R.A.5
-
33
-
-
0001737892
-
The effect of periodic habitat fluctuations on a nonlinear insect population model
-
S. M. HENSON AND J. M. CUSHING, The effect of periodic habitat fluctuations on a nonlinear insect population model, J. Math. Biol., 36 (1997), pp. 201-226.
-
(1997)
J. Math. Biol.
, vol.36
, pp. 201-226
-
-
Henson, S.M.1
Cushing, J.M.2
-
34
-
-
33847579397
-
Insect populations respond to fluctuating environments
-
D. JILLSON, Insect populations respond to fluctuating environments, Nature, 288 (1980), pp. 699-700.
-
(1980)
Nature
, vol.288
, pp. 699-700
-
-
Jillson, D.1
-
35
-
-
22544452119
-
A note on nonautonomous Beverton-Holt model
-
V. L. KOCIC, A note on nonautonomous Beverton-Holt model, J. Differential Equations Appl., 11 (2005), pp. 415-422.
-
(2005)
J. Differential Equations Appl.
, vol.11
, pp. 415-422
-
-
Kocic, V.L.1
-
36
-
-
3042510840
-
Global behavior of nonlinear difference equations of higher order with applications
-
Kluwer Academic Publishers, Dordrecht, The Netherlands
-
V. L. Kocic AND G. LADAS, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Math. Appl. 256, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993.
-
(1993)
Math. Appl.
, vol.256
-
-
Kocic, V.L.1
Ladas, G.2
-
37
-
-
3042647314
-
A note on attenuant cycles of population models with periodic carrying capacity
-
R. KON, A note on attenuant cycles of population models with periodic carrying capacity, J. Differential Equations Appl., 10 (2004), pp. 791-793.
-
(2004)
J. Differential Equations Appl.
, vol.10
, pp. 791-793
-
-
Kon, R.1
-
38
-
-
22544463638
-
Attenuant cycles of population models with periodic carrying capacity
-
R. KON, Attenuant cycles of population models with periodic carrying capacity, J. Differential Equations Appl., 11 (2005), pp. 423-430.
-
(2005)
J. Differential Equations Appl.
, vol.11
, pp. 423-430
-
-
Kon, R.1
-
39
-
-
0027077357
-
Periodic solutions of population models in a periodically fluctuating environment
-
J. LI, Periodic solutions of population models in a periodically fluctuating environment, Math. Biosci., 110 (1992), pp. 17-25.
-
(1992)
Math. Biosci.
, vol.110
, pp. 17-25
-
-
Li, J.1
-
40
-
-
0000336301
-
Bifurcations and dynamic complexity in simple ecological models
-
R. M. MAY AND G. F. OSTER, Bifurcations and dynamic complexity in simple ecological models, Amer. Naturalist, 110 (1976), pp. 573-579.
-
(1976)
Amer. Naturalist
, vol.110
, pp. 573-579
-
-
May, R.M.1
Oster, G.F.2
-
41
-
-
0017185443
-
Simple mathematical models with very complicated dynamics
-
R. M. MAY, Simple mathematical models with very complicated dynamics, Nature, 261 (1977), pp. 459-469.
-
(1977)
Nature
, vol.261
, pp. 459-469
-
-
May, R.M.1
-
43
-
-
84970543436
-
Compensatory reactions of populations to stresses, and their evolutionary significance
-
A. J. NICHOLSON, Compensatory reactions of populations to stresses, and their evolutionary significance, Aust. J. Zool., 2 (1954), pp. 1-65.
-
(1954)
Aust. J. Zool.
, vol.2
, pp. 1-65
-
-
Nicholson, A.J.1
-
45
-
-
0018830042
-
Population models in a periodically fluctuating environment
-
S. ROSENBLAT, Population models in a periodically fluctuating environment, J. Math. Biol., 9 (1980), pp. 23-36.
-
(1980)
J. Math. Biol.
, vol.9
, pp. 23-36
-
-
Rosenblat, S.1
-
46
-
-
0035888128
-
On the structure of attractors for discrete, periodically forced systems with applications to population models
-
J. F. BELGRADE AND H. D. ROBERDS, On the structure of attractors for discrete, periodically forced systems with applications to population models, Phys. D, 158 (2001), pp. 69-82.
-
(2001)
Phys. D
, vol.158
, pp. 69-82
-
-
Belgrade, J.F.1
Roberds, H.D.2
-
47
-
-
0034198679
-
A simple SIS epidemic model with a backward bifurcation
-
P. VAN DEN DRIESSCHE AND J. WATMOUGH, A simple SIS epidemic model with a backward bifurcation, J. Math. Biol., 40 (2000), pp. 525-540.
-
(2000)
J. Math. Biol.
, vol.40
, pp. 525-540
-
-
Van Den Driessche, P.1
Watmough, J.2
-
48
-
-
33750161457
-
Periodically forced nonlinear difference equations with delay
-
Difference Equations and Discrete Dynamical Systems, University of Southern California, L. Allen, B. Aulbach, S. Elaydi, and R. Sacker, eds., World Scientific, River Edge, NJ
-
A.-A. YAKUBU, Periodically forced nonlinear difference equations with delay, in Difference Equations and Discrete Dynamical Systems, Proceedings of the 9th International Conference, University of Southern California, L. Allen, B. Aulbach, S. Elaydi, and R. Sacker, eds., World Scientific, River Edge, NJ, 2005, pp. 217-231.
-
(2005)
Proceedings of the 9th International Conference
, pp. 217-231
-
-
Yakubu, A.-A.1
-
49
-
-
33750477302
-
Spatially discrete metapopulation models with directional dispersal
-
to appear
-
A.-A. YAKUBU AND M. FOGARTY, Spatially discrete metapopulation models with directional dispersal, Math. Biosci., to appear.
-
Math. Biosci.
-
-
Yakubu, A.-A.1
Fogarty, M.2
|