-
1
-
-
75449085144
-
Nicholsons blowflies differential equations revisited: Main results and open problems
-
doi:10.1016/j.apm.2009.08.027
-
Berezansky, L., Braverman, E. & Idels, L. 2010 Nicholsons blowflies differential equations revisited: main results and open problems. Appl. Math. Model. 34, 1405-1417. (doi:10.1016/j.apm.2009.08.027)
-
(2010)
Appl. Math. Model
, vol.34
, pp. 1405-1417
-
-
Berezansky, L.1
Braverman, E.2
Idels, L.3
-
2
-
-
0022180238
-
Interaction of spatial diffusion and delays in models of genetic control by repression
-
DOI 10.1007/BF00276489
-
Busenberg, S. & Mahaffy, J. 1985 Interaction of spatial diffusion and delays in models of genetic control by repression. J. Math. Biol. 22, 313-333. (doi:10.1007/BF00276489) (Pubitemid 16254227)
-
(1985)
Journal of Mathematical Biology
, vol.22
, Issue.3
, pp. 313-333
-
-
Busenberg, S.1
Mahaffy, J.2
-
3
-
-
0033209987
-
Interaction of maturation delay and nonlinear birth in population and epidemic models
-
doi:10.1007/s002850050194
-
Cooke, K., van den Driessche, P. & Zou, X. 1999 Interaction of maturation delay and nonlinear birth in population and epidemic models. J. Math. Biol. 39, 332-352. (doi:10.1007/s002850050194
-
(1999)
J. Math. Biol.
, vol.39
, pp. 332-352
-
-
Cooke, K.1
Van Den Driessche, P.2
Zou, X.3
-
4
-
-
0003095221
-
The solution of equations by iteration
-
doi:10.1017/S030500410002990X
-
Coppel, W. A. 1955 The solution of equations by iteration. Proc. Camb. Phil. Soc. 51, 41-43. (doi:10.1017/S030500410002990X)
-
(1955)
Proc. Camb. Phil. Soc.
, vol.51
, pp. 41-43
-
-
Coppel, W.A.1
-
5
-
-
33947512017
-
Population models: Stability in one dimension
-
DOI 10.1007/s11538-006-9129-1
-
Cull, P. 2007 Population models: stability in one dimension. Bull. Math. Biol. 69, 989-1017. (doi:10.1007/s11538-006-9129-1) (Pubitemid 46466304)
-
(2007)
Bulletin of Mathematical Biology
, vol.69
, Issue.3
, pp. 989-1017
-
-
Cull, P.1
-
6
-
-
33644673010
-
Asymptotic stability for delayed logistic type equations
-
DOI 10.1016/j.mcm.2005.11.006, PII S0895717705005674
-
Faria, T. 2006 Asymptotic stability for delayed logistic type equations. Math. Comput. Model. 43, 433-445. (doi:10.1016/j.mcm.2005.11.006) (Pubitemid 43330871)
-
(2006)
Mathematical and Computer Modelling
, vol.43
, Issue.3-4
, pp. 433-445
-
-
Faria, T.1
-
7
-
-
0002257093
-
Convergence to equilibrium for delay-diffusion equations with small delay
-
doi:10.1007/BF01063736
-
Friesecke, G. 1993 Convergence to equilibrium for delay-diffusion equations with small delay. J. Dyn. Differ. Equ. 5, 89-103. (doi:10.1007/ BF01063736)
-
(1993)
J. Dyn. Differ. Equ.
, vol.5
, pp. 89-103
-
-
Friesecke, G.1
-
8
-
-
84879144864
-
A note on global attractivity in models of hematopoiesis
-
doi:10.1007/BF02514684
-
Gopalsamy, K., Trofimchuk, S. & Bantsur, N. 1998 A note on global attractivity in models of hematopoiesis. Ukrainian Math. J. 50, 3-12. (doi:10.1007/BF02514684)
-
(1998)
Ukrainian Math. J.
, vol.50
, pp. 3-12
-
-
Gopalsamy, K.1
Trofimchuk, S.2
Bantsur, N.3
-
9
-
-
0002702117
-
Nicholson's blowflies revisited
-
doi:10.1038/287017a0
-
Gurney, W. S. C, Blythe, S. P. & Nisbet, R. M. 1980 Nicholson's blowflies revisited. Nature 287, 17-21. (doi:10.1038/287017a0
-
(1980)
Nature
, vol.287
, pp. 17-21
-
-
Gurney, W.S.C.1
Blythe, S.P.2
Nisbet, R.M.3
-
10
-
-
0000103184
-
Global attractivity in x′ (t) = -δx (t) + pf (x (t (t - τ)))
-
Györi, I. & Trofimchuk, S. 1999 Global attractivity in x′ (t) = -δx (t) + pf (x (t (t - τ))). Dyn. Syst. Appl. 8, 197-210.
-
(1999)
Dyn. Syst. Appl.
, vol.8
, pp. 197-210
-
-
Györi, I.1
Trofimchuk, S.2
-
11
-
-
0003293929
-
Asymptotic behavior of dissipative systems
-
Providence, RI: American Mathematical Society
-
Hale, J. 1988 Asymptotic behavior of dissipative systems. Mathematics Survey Monographs 20. Providence, RI: American Mathematical Society.
-
(1988)
Mathematics Survey Monographs
, vol.20
-
-
Hale, J.1
-
13
-
-
84960560867
-
Roots of the transcendental equation associated with a certain differential difference equations
-
doi:10.1112/jlms/s1-25.3.226
-
Hayes, N. D. 1950 Roots of the transcendental equation associated with a certain differential difference equations. J. Lond. Math. Soc. 25, 226-232. (doi:10.1112/jlms/s1-25.3.226)
-
(1950)
J. Lond. Math. Soc.
, vol.25
, pp. 226-232
-
-
Hayes, N.D.1
-
14
-
-
0000497896
-
Global Dynamics for a Reaction-Diffusion Equation with Time Delay
-
DOI 10.1006/jdeq.1997.3374, PII S002203969793374X
-
Huang, W. 1998 Global dynamics for a reaction-diffusion equation with time delay. J. Differ. Equ. 143, 293-326. (doi:10.1006/jdeq.1997.3374) (Pubitemid 128347464)
-
(1998)
Journal of Differential Equations
, vol.143
, Issue.2
, pp. 293-326
-
-
Huang, W.1
-
16
-
-
0012088132
-
Stable steady state of some population models
-
doi:10.1007/BF01048159
-
Karakostas, G., Philos, C. G. & Sficas, Y. C. 1992 Stable steady state of some population models. J. Dynam. Diff Equ. 4, 161-190. (doi:10.1007/BF01048159)
-
(1992)
J. Dynam. Diff Equ.
, vol.4
, pp. 161-190
-
-
Karakostas, G.1
Philos, C.G.2
Sficas, Y.C.3
-
17
-
-
40449089355
-
Global dynamics of delay differential equations
-
doi:10.1007/s10998-008-5083-x
-
Krisztin, T. 2008 Global dynamics of delay differential equations. Period. Math. Hung. 56, 83-95. (doi:10.1007/s10998-008-5083-x)
-
(2008)
Period. Math. Hung.
, vol.56
, pp. 83-95
-
-
Krisztin, T.1
-
18
-
-
0003265680
-
Shape, smoothness and invariant stratification of an attracting set for delayed monotone positive feedback
-
Providence, RI: American Mathematical Society
-
Krisztin, T., Walther, H.-O. & Wu, J. 1999 Shape, smoothness and invariant stratification of an attracting set for delayed monotone positive feedback. Fields Institute Monographs 11. Providence, RI: American Mathematical Society.
-
(1999)
Fields Institute Monographs
, vol.11
-
-
Krisztin, T.1
Walther, H.-O.2
Wu, J.3
-
20
-
-
0023635696
-
Linearized oscillations in population dynamics
-
Kulenovic, N. M. R. S. & Ladas, G. 1987 Linearized oscillations in population dynamics. Bull. Math. Biol. 49, 615-627.
-
(1987)
Bull. Math. Biol.
, vol.49
, pp. 615-627
-
-
Kulenovic, N.M.R.S.1
Ladas, G.2
-
21
-
-
30144437959
-
Four theorems and one conjecture on the global asymptotic stability of delay differential equations
-
eds M. Delgado et al., Singapore: World Scientific
-
Liz, E. 2004 Four theorems and one conjecture on the global asymptotic stability of delay differential equations. In The first 60 years of nonlinear analysis of Jean Mawhin (eds M. Delgado et al.), pp. 117-129. Singapore: World Scientific.
-
(2004)
The First 60 Years of Nonlinear Analysis of Jean Mawhin
, pp. 117-129
-
-
Liz, E.1
-
22
-
-
33847750617
-
Local stability implies global stability in some one-dimensional discrete single-species models
-
Liz, E. 2007 Local stability implies global stability in some one-dimensional discrete single-species models. Discrete Contin. Dyn. Syst. Ser. B 7, 191-199.
-
(2007)
Discrete Contin. Dyn. Syst. Ser. B.
, vol.7
, pp. 191-199
-
-
Liz, E.1
-
23
-
-
69549111437
-
On the global attractivity of delay differential equations with unimodel feedback
-
doi:10.3934/dcds.2009.24.1215
-
Liz, E. & Röst, G. 2009 On the global attractivity of delay differential equations with unimodel feedback. Discrete. Contin. Dyn. Syst. 24, 1215-1224. (doi:10.3934/dcds.2009.24.1215)
-
(2009)
Discrete. Contin. Dyn. Syst.
, vol.24
, pp. 1215-1224
-
-
Liz, E.1
Röst, G.2
-
24
-
-
85020822589
-
Dichotomy results for delay differential equations with negative Schwarzian derivative
-
In press
-
Liz, E. & Röst, G. In press. Dichotomy results for delay differential equations with negative Schwarzian derivative. Nonlinear Anal. RWA.
-
Nonlinear Anal. RWA
-
-
Liz, E.1
Röst, G.2
-
25
-
-
0017714604
-
Oscillation and chaos in physiological control systems
-
doi:10.1126/science.267326
-
Mackey, M. C. & Glass, L. 1977 Oscillation and chaos in physiological control systems. Science 197, 287-289. (doi:10.1126/science.267326)
-
(1977)
Science
, vol.197
, pp. 287-289
-
-
Mackey, M.C.1
Glass, L.2
-
26
-
-
0001842517
-
Global continuation and asymptotic behaviour for periodic solutions of a differential-delay equation
-
doi:10.1007/BF01790539
-
Mallet-Paret, J. & Nussbaum, R. 1986 Global continuation and asymptotic behaviour for periodic solutions of a differential-delay equation. Ann. Math. Pura Appl. 145, 33-128. (doi:10.1007/BF01790539
-
(1986)
Ann. Math. Pura Appl.
, vol.145
, pp. 33-128
-
-
Mallet-Paret, J.1
Nussbaum, R.2
-
27
-
-
84966246501
-
Abstract functional differential equations and reaction-diffusion systems
-
doi:10.2307/2001590
-
Martin, R. & Smith, H. L. 1990 Abstract functional differential equations and reaction-diffusion systems. Trans. Am. Math. Soc. 321, 1-44. (doi:10.2307/2001590)
-
(1990)
Trans. Am. Math. Soc.
, vol.321
, pp. 1-44
-
-
Martin, R.1
Smith, H.L.2
-
28
-
-
0001989035
-
Reaction-diffusion systems with time delay: Monotonicity, invariance, comparison and convergence
-
Martin, R. & Smith, H. L. 1991 Reaction-diffusion systems with time delay: monotonicity, invariance, comparison and convergence. J. Reine Angew. Math. 413, 1-35.
-
(1991)
J. Reine Angew. Math.
, vol.413
, pp. 1-35
-
-
Martin, R.1
Smith, H.L.2
-
29
-
-
3242678973
-
Asymptotic stability of travelling waves for Nicholson's blowflies equation with diffusion
-
doi:10.1017/S0308210500003358
-
Mei, M., So, J. W.-H., Li, M. Y. & Shen, S. 2004 Asymptotic stability of travelling waves for Nicholson's blowflies equation with diffusion. Proc. R. Soc. Edinb. Sect. A 134, 579-594. (doi:10.1017/S0308210500003358)
-
(2004)
Proc. R. Soc. Edinb. Sect. A
, vol.134
, pp. 579-594
-
-
Mei, M.1
So, J.W.-H.2
Li, M.Y.3
Shen, S.4
-
30
-
-
84970556051
-
An outline of the dynamics of animal populations
-
doi:10.1071/ZO9540009
-
Nicholson, A. J. 1954 An outline of the dynamics of animal populations. Aust. J. Zool. 2, 9-65. (doi:10.1071/ZO9540009
-
(1954)
Aust. J. Zool.
, vol.2
, pp. 9-65
-
-
Nicholson, A.J.1
-
31
-
-
36348976487
-
Domain-decomposition method for the global dynamics of delay differential equations with unimodal feedback
-
doi:10.1098/rspa.2007.1890
-
Röst, G. & Wu, J. 2007 Domain-decomposition method for the global dynamics of delay differential equations with unimodal feedback. Proc. R. Soc. A 463, 2655-2669. (doi:10.1098/rspa.2007.1890
-
(2007)
Proc. R. Soc. A
, vol.463
, pp. 2655-2669
-
-
Röst, G.1
Wu, J.2
-
32
-
-
0001273984
-
Stable orbits and bifurcation of maps of the interval
-
doi:10.1137/0135020
-
Singer, D. 1978 Stable orbits and bifurcation of maps of the interval. SIAM J. Appl. Math. 35 260-267. (doi:10.1137/0135020)
-
(1978)
SIAM J. Appl. Math.
, vol.35
, pp. 260-267
-
-
Singer, D.1
-
33
-
-
0001219328
-
Dirichlet Problem for the Diffusive Nicholson's Blowflies Equation
-
DOI 10.1006/jdeq.1998.3489, PII S0022039698934891
-
So, J. W.-H. & Yang, Y. 1998 Dirichlet problem for the diffusive Nicholson's blowflies equation. J. Differ. Equ. 150, 317-348. (doi:10.1006/jdeq.1998.3489) (Pubitemid 128345992)
-
(1998)
Journal of Differential Equations
, vol.150
, Issue.2
, pp. 317-348
-
-
So, J.W.-H.1
Yang, Y.2
-
34
-
-
0040577509
-
Global attractivity and uniform persistence in Nicholson's blowflies
-
So, J. W.-H. & Yu, J. S. 1994 Global attractivity and uniform persistence in Nicholson's blowflies. Differ. Equ. Dyn. Syst. 2, 11-18.
-
(1994)
Differ. Equ. Dyn. Syst.
, vol.2
, pp. 11-18
-
-
So, J.W.-H.1
Yu, J.S.2
-
35
-
-
0035882630
-
Traveling waves for the diffusive Nicholson's blowflies equation
-
doi:10.1016/S0096-3003 00 00055-2
-
So, J. W.-H. & Zou, X. 2001 Traveling waves for the diffusive Nicholson's blowflies equation. Appl. Math. Comput. 122, 385-392. (doi:10.1016/S0096-3003 (00) 00055-2)
-
(2001)
Appl. Math. Comput.
, vol.122
, pp. 385-392
-
-
So, J.W.-H.1
Zou, X.2
-
36
-
-
32044440101
-
A reaction-diffusion model for a single species with age structure. I. Travelling wavefronts on unbounded domains
-
doi:10.1098/rspa.2001.0789
-
So, J. W.-H., Wu, J. & Zou, X. 2001 A reaction-diffusion model for a single species with age structure. I. Travelling wavefronts on unbounded domains. Proc. R. Soc. Lond. A 457, 1841-1853. (doi:10.1098/rspa.2001.0789)
-
(2001)
Proc. R. Soc. Lond. A
, vol.457
, pp. 1841-1853
-
-
So, J.W.-H.1
Wu, J.2
Zou, X.3
-
37
-
-
0141922770
-
Stability of scalar delay differential equations with dominant delayed terms
-
doi:10.1017/S0308210500002766
-
Tang, X. H. & Zou, X. 2003 Stability of scalar delay differential equations with dominant delayed terms. Proc. R. Soc. Edinb. A 133, 951-968. (doi:10.1017/S0308210500002766)
-
(2003)
Proc. R. Soc. Edinb. A
, vol.133
, pp. 951-968
-
-
Tang, X.H.1
Zou, X.2
-
38
-
-
84968492827
-
Existence and stability for partial functional differential equations
-
doi:10.2307/1997265
-
Travis, C. C. & Webb, G. F. 1974 Existence and stability for partial functional differential equations. Trans. Am. Math. Soc. 200, 395-418. (doi:10.2307/1997265)
-
(1974)
Trans. Am. Math. Soc.
, vol.200
, pp. 395-418
-
-
Travis, C.C.1
Webb, G.F.2
-
39
-
-
0003195186
-
The 2-dimensional attractor of x′ (t) = -x (t) + f (x (t - 1))
-
Walther, H.-O. 1995 The 2-dimensional attractor of x′ (t) = -x (t) + f (x (t - 1)). Mem. Am. Math. Soc. 113, 544.
-
(1995)
Mem. Am. Math. Soc.
, vol.113
, pp. 544
-
-
Walther, H.-O.1
-
40
-
-
12244312783
-
Hopf bifurcation analysis in a delayed Nicholson blowflies equation
-
DOI 10.1016/j.na.2003.04.002, PII S0362546X04005255
-
Wei, J. & Li, M. Y. 2005 Hopf bifurcation analysis in a delayed Nicholson blowflies equation. Nonlinear Anal. 60, 1351-1367. (doi:10.1016/j.na.2003.04.002) (Pubitemid 40114281)
-
(2005)
Nonlinear Analysis, Theory, Methods and Applications
, vol.60
, Issue.7
, pp. 1351-1367
-
-
Wei, J.1
Li, M.Y.2
-
41
-
-
0003345730
-
Theory and applications of partial functional differential equations
-
New York, NY: Springer
-
Wu, J. 1996 Theory and applications of partial functional differential equations. Applied Mathematical Sciences, vol. 119. New York, NY: Springer.
-
(1996)
Applied Mathematical Sciences
, vol.119
-
-
Wu, J.1
-
42
-
-
0343717093
-
Traveling wave fronts of reaction-diffusion systems with delay
-
doi:10.1023/A:1016690424892
-
Wu, J. & Zou, X. 2001 Traveling wave fronts of reaction-diffusion systems with delay. J. Dyn. Differ. Equ. 13, 651-687. (doi:10.1023/A: 1016690424892)
-
(2001)
J. Dyn. Differ. Equ.
, vol.13
, pp. 651-687
-
-
Wu, J.1
Zou, X.2
-
43
-
-
3242726256
-
Dynamics for the diffusive Nicholson's blowflies equation
-
Springfield, MO, 29 May-1 June
-
Yang, Y. & So, J. W.-H. 1996 Dynamics for the diffusive Nicholson's blowflies equation. In Proc. of Int. Conf. on Dynamical Systems and Differential Equations, Springfield, MO, 29 May-1 June, vol. II.
-
(1996)
Proc. of Int. Conf. on Dynamical Systems and Differential Equations
, vol.2
-
-
Yang, Y.1
So, J.W.-H.2
-
44
-
-
53349160548
-
Global attractivity of the diffusive Nicholson blowflies equation with Neumann boundary condition: A non-monotone case
-
doi:10.1016/j.jde.2008.03.007
-
Yi, T. & Zou, X. 2008 Global attractivity of the diffusive Nicholson blowflies equation with Neumann boundary condition: a non-monotone case. J. Differ. Equ. 245, 3376-3388. (doi:10.1016/j.jde.2008.03.007)
-
(2008)
J. Differ. Equ.
, vol.245
, pp. 3376-3388
-
-
Yi, T.1
Zou, X.2
-
45
-
-
77958088036
-
Threshold dynamics of a delayed reaction diffusion equation subject to the Dirichlet condition
-
doi:10.1080/17513750802425656
-
Yi, T., Chen, Y. & Wu, J. 2009 Threshold dynamics of a delayed reaction diffusion equation subject to the Dirichlet condition. J. Biol. Dyn. 3, 331-341. (doi:10.1080/17513750802425656)
-
(2009)
J. Biol. Dyn
, vol.3
, pp. 331-341
-
-
Yi, T.1
Chen, Y.2
Wu, J.3
|