-
1
-
-
0025132577
-
A time-delay model of single-species growth with stage structure
-
DOI 10.1016/0025-5564(90)90019-U
-
W. Aiello and H. I. Freedman, A time-delay model of single-species growth with stage struc-ture, Math. Biosci., 101 (1990), 139-153. (Pubitemid 20357965)
-
(1990)
Mathematical Biosciences
, vol.101
, Issue.2
, pp. 139-153
-
-
Aiello, W.G.1
Freedman, H.I.2
-
2
-
-
0001687872
-
Analysis of a model representing stage-structured population growth with state-dependent time delay
-
W. Aiello, H. I. Freedman and J. Wu, Analysis of a model representing stage-structured population growth with state-dependent time delay, SIAM J. Appl. Math., 52 (1992), 855-869.
-
(1992)
SIAM J. Appl. Math.
, vol.52
, pp. 855-869
-
-
Aiello, W.1
Freedman, H.I.2
Wu, J.3
-
3
-
-
33744519822
-
An alternative formulation for a delayed logistic equation
-
DOI 10.1016/j.jtbi.2005.11.007, PII S002251930500490X
-
J. Arino, L. Wang and G. S. K. Wolkowicz, An alternative formulation for a delayed logistic equation, J. Theore. Biol., 241 (2006), 109-119. (Pubitemid 43817987)
-
(2006)
Journal of Theoretical Biology
, vol.241
, Issue.1
, pp. 109-119
-
-
Arino, J.1
Wang, L.2
Wolkowicz, G.S.K.3
-
4
-
-
0016755044
-
Time delays are not necessarily destabilizing
-
J. R. Beddington and R. M. May, Time delays are not necessarily destabilizing, Math. Biosci., 27 (1975), 109-117.
-
(1975)
Math. Biosci.
, vol.27
, pp. 109-117
-
-
Beddington, J.R.1
May, R.M.2
-
5
-
-
0009677529
-
Sufficient conditions for stability of linear differential equations with distributed delay
-
S. Bernard, J. Bélair and M. C. Mackey, Sučient conditions for stability of linear differential equations with distributed delay, Disc. Cont. Dyn. Syst. Ser. B, 1 (2001), 233-256. (Pubitemid 33771907)
-
(2001)
Discrete and Continuous Dynamical Systems - Series B
, vol.1
, Issue.2
, pp. 233-256
-
-
Bernard, S.1
Belair, J.2
Mackey, M.G.3
-
6
-
-
0000518471
-
Instability and complex dynamic behavior in population models with long time delays
-
S. P. Blythe, R. M. Nisbet and W. S. C. Gurney, Instability and complex dynamic behavior in population models with long time delays, Theor. Pop. Biol., 22 (1982), 147-176.
-
(1982)
Theor. Pop. Biol.
, vol.22
, pp. 147-176
-
-
Blythe, S.P.1
Nisbet, R.M.2
Gurney, W.S.C.3
-
7
-
-
37149037748
-
Three types of simple DDE's describing tumor growth
-
M. Bodnar and U. Foryś, Three types of simple DDE's describing tumor growth, J. Biol. Systems, 15 (2007), 1-19.
-
(2007)
J. Biol. Systems
, vol.15
, pp. 1-19
-
-
Bodnar, M.1
Foryś, U.2
-
8
-
-
46749151431
-
Global stability and Hopf bifurcation for a gerneral class of delay differential equations
-
M. Bodnar and U. Foryś, Global stability and Hopf bifurcation for a gerneral class of delay differential equations, Math. Mathods Appl. Sci., 31 (2008), 1197-1207.
-
(2008)
Math. Mathods Appl. Sci.
, vol.31
, pp. 1197-1207
-
-
Bodnar, M.1
Foryś, U.2
-
9
-
-
38249033593
-
Stability of stage-structured population models
-
F. Brauer and Z. Ma, Stability of stage-structured population models, J. Math. Anal. Appl., 126 (1987), 301-315.
-
(1987)
J. Math. Anal. Appl.
, vol.126
, pp. 301-315
-
-
Brauer, F.1
Ma, Z.2
-
10
-
-
0003209221
-
Mathematical models in population biology and epidemiology
-
Springer-Verlag, New York
-
F. Brauer and C. Castillo-Chávez, "Mathematical Models in Population Biology and Epidemiology," Texts in Applied Mathematics, 40, Springer-Verlag, New York, 2001.
-
(2001)
Texts in Applied Mathematics
, vol.40
-
-
Brauer, F.1
Castillo-Chávez, C.2
-
11
-
-
84863886649
-
Asymptotic stability for functional differential equations
-
T. A. Burton and G. Makey, Asymptotic stability for functional differential equations, J. Math. Anal. Appl., 126 (1994), 301-315.
-
(1994)
J. Math. Anal. Appl.
, vol.126
, pp. 301-315
-
-
Burton, T.A.1
Makey, G.2
-
12
-
-
84863911352
-
Marachkov type stability results for functional-differential equa-tions
-
T. A. Burton and G. Makey, Marachkov type stability results for functional-differential equa-tions, E. J. Qualitative Theory of Diff. Equ., 1998, 17 pp.
-
(1998)
E. J. Qualitative Theory of Diff. Equ.
, pp. 17
-
-
Burton, T.A.1
Makey, G.2
-
13
-
-
0033209987
-
Interaction of maturation delay and nonlinear birth in population and epidemic models
-
K. Cooke, P. van den Driessche and X. Zou, Interaction of maturation delay and nonlinear birth in population and epidemic models, J. Math. Biol., 39 (1999), 332-352.
-
(1999)
J. Math. Biol.
, vol.39
, pp. 332-352
-
-
Cooke, K.1
Van Den Driessche, P.2
Zou, X.3
-
14
-
-
77950267897
-
Stability and Hopf bifurcation for a first-order delay differential equation with distributed delay
-
Understanding Complex Systems, Springer, Berlin
-
F. Crauste, Stability and Hopf bifurcation for a first-order delay differential equation with distributed delay, in "Complex Time-Delay Systems," Understanding Complex Systems, Springer, Berlin, (2010), 263-296.
-
(2010)
Complex Time-Delay Systems
, pp. 263-296
-
-
Crauste, F.1
-
15
-
-
0017740956
-
Time delays in single species growth models
-
J. M. Cushing, Time delays in single growth models, J. Math. Biol., 4 (1977), 257-264. (Pubitemid 8139222)
-
(1977)
Journal of Mathematical Biology
, vol.4
, Issue.3
, pp. 257-264
-
-
Cushing, J.M.1
-
16
-
-
0022842682
-
Global stability in time-delayed single-species dynamics
-
H. I. Freedman and K. Gopalsamy, Global stability in time-delayed single-species dynamics, Bull. Math. Biol., 48 (1986), 485-492.
-
(1986)
Bull. Math. Biol.
, vol.48
, pp. 485-492
-
-
Freedman, H.I.1
Gopalsamy, K.2
-
17
-
-
3242720484
-
Global stability for a class of delay differential equations
-
U. Foryś, Global stability for a class of delay differential equations, Appl. Math. Lett., 17 (2004), 581-584.
-
(2004)
Appl. Math. Lett.
, vol.17
, pp. 581-584
-
-
Foryś, U.1
-
18
-
-
0003248828
-
Stability and oscillations in delay differential equations of population dynamics
-
Kluwer Academic Publishers Group, Dordrecht
-
K. Gopalsamy, "Stability and Oscillations in Delay Differential Equations of Population Dynamics," Mathematics and its Applications, 74, Kluwer Academic Publishers Group, Dordrecht, 1992.
-
(1992)
Mathematics and its Applications
, vol.74
-
-
Gopalsamy, K.1
-
19
-
-
48749143053
-
Liapunov-Razumikhin functions and an invariance principle for functional-differential equations
-
J. R. Haddock and J. Terjéki, Liapunov-Razumikhin functions and an invariance principle for functional-differential equations, J. Diff. Equat., 48 (1983), 95-122.
-
(1983)
J. Diff. Equat.
, vol.48
, pp. 95-122
-
-
Haddock, J.R.1
Terjéki, J.2
-
20
-
-
0003492060
-
-
Second editon, Applied Mathematical Sciences, Springer-Verlag, New York-Heidelberg
-
J. K. Hale, "Theory of Functional Differential Equations," Second editon, Applied Mathematical Sciences, Vol. 3, Springer-Verlag, New York-Heidelberg, 1977.
-
(1977)
Theory of Functional Differential Equations
, vol.3
-
-
Hale, J.K.1
-
21
-
-
84863957227
-
Asymptotic stability conditions for a linear nonautonomous delay differential equation
-
(eds. M. Martelli K. Cooke E. Cumberbatch R. Tang and H. Thieme) (Claremont CA 1994), World Sci. Publ., River Edge, NJ
-
L. Hatvani, Asymptotic stability conditions for a linear nonautonomous delay differential equation, in "Differential Equations and Applications to Biology and to Industry" (eds. M. Martelli, K. Cooke, E. Cumberbatch, R. Tang and H. Thieme) (Claremont, CA, 1994), World Sci. Publ., River Edge, NJ, (1996), 181-190.
-
(1996)
Differential Equations and Applications to Biology and to Industry
, pp. 181-190
-
-
Hatvani, L.1
-
22
-
-
84960560867
-
Roots of the transcendental equation associated with a certain difference-differential equation
-
N. D. Hayes, Roots of the transcendental equation associated with a certain difference-differential equation, J. London Math. Society, 25 (1950), 226-232.
-
(1950)
J. London Math. Society
, vol.25
, pp. 226-232
-
-
Hayes, N.D.1
-
23
-
-
77954623221
-
Global stability for delay SIR and SEIR epidemic models with nonlinear incidence rate
-
G. Huang, Y. Takeuchi, W. Ma and D.Wei, Global Stability for delay SIR and SEIR epidemic models with nonlinear incidence rate, Bull. Math. Biol., 72 (2010), 1192-1207.
-
(2010)
Bull. Math. Biol.
, vol.72
, pp. 1192-1207
-
-
Huang, G.1
Takeuchi, Y.2
Ma, W.3
Wei, D.4
-
24
-
-
77956236840
-
Lyapunov functionals for delay differential equations model for viral infections
-
G. Huang, Y. Takeuchi and W. Ma, Lyapunov functionals for delay differential equations model for viral infections, SIAM J. Appl. Math., 70 (2010), 2693-2708.
-
(2010)
SIAM J. Appl. Math.
, vol.70
, pp. 2693-2708
-
-
Huang, G.1
Takeuchi, Y.2
Ma, W.3
-
25
-
-
0012088132
-
Stable steady state of some population models
-
G. Karakostas, Ch. G. Philos and Y. G. Sčas, Stable steady state of some population models, J. Dynam. Differential Equations, 4 (1992), 161-190.
-
(1992)
J. Dynam. Differential Equations
, vol.4
, pp. 161-190
-
-
Karakostas, G.1
Philos, C.G.2
Sčas, Y.G.3
-
26
-
-
0036170039
-
Oscillation and stability in nonlinear delay differential equations of population dynamics
-
DOI 10.1016/S0895-7177(01)00166-2, PII S0895717701001662
-
I. Kubiaczyk and S. H. Saker, Oscillation and stability in nonlinear delay differntial equations of population dynamics, Math. Comput. Model., 35 (2002), 295-301. (Pubitemid 34147308)
-
(2002)
Mathematical and Computer Modelling
, vol.35
, Issue.3-4
, pp. 295-301
-
-
Kubiaczyk, I.1
Saker, S.H.2
-
27
-
-
0010395113
-
Global attractivity in delay defferential equations related to models of physiology and population biology
-
Y. Kuang, Global attractivity in delay defferential equations related to models of physiology and population biology, Japan J. Indust. Appl. Math., 9 (1992), 205-238.
-
(1992)
Japan J. Indust. Appl. Math.
, vol.9
, pp. 205-238
-
-
Kuang, Y.1
-
28
-
-
0003302813
-
Delay differential equations with applications in population dynamics
-
Academic Press, Inc., Boston, MA
-
Y. Kuang, "Delay Differential Equations with Applications in Population Dynamics," Mathematics in Science and Engineering, 191, Academic Press, Inc., Boston, MA, 1993.
-
(1993)
Mathematics in Science and Engineering
, vol.191
-
-
Kuang, Y.1
-
29
-
-
84968497717
-
Global stability of a biological model with time delay
-
S. M. Lenhart and C. C. Travis, Global stability of a biological model with time delay, Proc. Amer. Math. Soc., 96 (1986), 75-78.
-
(1986)
Proc. Amer. Math. Soc.
, vol.96
, pp. 75-78
-
-
Lenhart, S.M.1
Travis, C.C.2
-
30
-
-
0017714604
-
Oscillation and chaos in physiological control systems
-
M. C. Mackey and L. Glass, Oscillation and chaos in physiological control systems, Science, 197 (1977), 287-289. (Pubitemid 8130447)
-
(1977)
Science
, vol.197
, Issue.4300
, pp. 287-289
-
-
Mackey, M.C.1
Glass, L.2
-
31
-
-
84970556051
-
An outline of the dynamics of animal populations
-
A. J. Nicholson, An outline of the dynamics of animal populations, Austral. J. Zoo., 2 (1954), 9-65.
-
(1954)
Austral. J. Zoo.
, vol.2
, pp. 9-65
-
-
Nicholson, A.J.1
-
32
-
-
34248517099
-
Delay differential equations in single species dynamics
-
(eds. O. Arino E. Ait Dads and M. Hbid) NATO Sci. Ser. II Math. Phys. Chem. 205 Springer, Dordrecht
-
S. Ruan, Delay differential equations in single species dynamics, in "Delay Differential Equations and Applications" (eds. O. Arino, E. Ait Dads and M. Hbid), NATO Sci. Ser. II Math. Phys. Chem., 205, Springer, Dordrecht, (2006), 477-517.
-
(2006)
Delay Differential Equations and Applications
, pp. 477-517
-
-
Ruan, S.1
-
33
-
-
36348976487
-
Domain-decomposition method for the global dynamics of delay differen-tial equations with unimodal feedback
-
G. Röst and J. Wu, Domain-decomposition method for the global dynamics of delay differen-tial equations with unimodal feedback, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 463 (2007), 2655-2669.
-
(2007)
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.
, vol.463
, pp. 2655-2669
-
-
Röst, G.1
Wu, J.2
-
34
-
-
80052187016
-
An introduction to delay differential equations with applications to the life sciences
-
Springer, New York, 2011
-
H. Smith, "An Introduction to Delay Differential Equations with Applications to the Life Sciences," Texts in Applied Mathematics, 57, Springer, New York, 2011.
-
Texts in Applied Mathematics
, vol.57
-
-
Smith, H.1
-
35
-
-
0342349150
-
Oscillations in housey population sizes due to time lags
-
C. E. Taylor and R. R. Sokal, Oscillations in housey population sizes due to time lags, Ecology, 57 (1976), 1060-1067.
-
(1976)
Ecology
, vol.57
, pp. 1060-1067
-
-
Taylor, C.E.1
Sokal, R.R.2
-
36
-
-
0003195186
-
The 2-dimensional attractor of x'(t) = -μx(t)+f(x(t-1)
-
H.-O. Walther, The 2-dimensional attractor of x'(t) = -μx(t)+f(x(t-1)), Mem. Am. Math. Soc., 113 (1995), vi+76 pp.
-
(1995)
Mem. Am. Math. Soc.
, vol.113
-
-
Walther, H.-O.1
|