-
1
-
-
0038778726
-
Global bifurcation in the Brusselator system
-
K.J. Brown, F.A. Davidson, Global bifurcation in the Brusselator system, Nonlinear Anal. TMA 24 (1995) 1713-1725.
-
(1995)
Nonlinear Anal. TMA
, vol.24
, pp. 1713-1725
-
-
Brown, K.J.1
Davidson, F.A.2
-
2
-
-
4344574613
-
-
Springer-Verlag/CIME, Berlin/Florence
-
V. Capasso, O. Diekmann (Eds.), Lecture Notes in Mathematics, vol. 1714, Springer-Verlag/CIME, Berlin/Florence, 1999.
-
(1999)
Lecture Notes in Mathematics
, vol.1714
-
-
Capasso, V.1
Diekmann, O.2
-
3
-
-
1542720931
-
Stationary patterns created by cross-diffusion for the competitor-competitor-mutualist model
-
W.Y. Chen, R. Peng, Stationary patterns created by cross-diffusion for the competitor-competitor-mutualist model, J. Math. Anal. Appl. 291 (2004) 550-564.
-
(2004)
J. Math. Anal. Appl.
, vol.291
, pp. 550-564
-
-
Chen, W.Y.1
Peng, R.2
-
5
-
-
12044252828
-
Pattern formation outside of equilibrium
-
M.C. Cross, P.S. Hohenberg, Pattern formation outside of equilibrium, Rev. Modern Phys. 65 (1993) 851-1112.
-
(1993)
Rev. Modern Phys.
, vol.65
, pp. 851-1112
-
-
Cross, M.C.1
Hohenberg, P.S.2
-
6
-
-
0037243354
-
Effects of certain degeneracies in the predator-prey model
-
E.N. Dancer, Y.H. Du, Effects of certain degeneracies in the predator-prey model, SIAM J. Math. Anal. 34 (2) (2002) 292-314.
-
(2002)
SIAM J. Math. Anal.
, vol.34
, Issue.2
, pp. 292-314
-
-
Dancer, E.N.1
Du, Y.H.2
-
7
-
-
23044517800
-
A priori bounds and global existence of solutions of the steady-state Sel'kov model
-
F.A. Davidson, B.P. Rynne, A priori bounds and global existence of solutions of the steady-state Sel'kov model, Proc. R. Soc. Edinburgh A 130 (2000) 507-516.
-
(2000)
Proc. R. Soc. Edinburgh A
, vol.130
, pp. 507-516
-
-
Davidson, F.A.1
Rynne, B.P.2
-
8
-
-
0001674774
-
S-shaped global bifurcation curve and Hopf bifurcation of positive solutions to a predator-prey model
-
Y.H. Du, Y. Lou, S-shaped global bifurcation curve and Hopf bifurcation of positive solutions to a predator-prey model, J. Differential Equations 144 (2) (1998) 390-440.
-
(1998)
J. Differential Equations
, vol.144
, Issue.2
, pp. 390-440
-
-
Du, Y.H.1
Lou, Y.2
-
9
-
-
23044527512
-
Qualitative behavior of positive solutions of a predator-prey model: Effects of saturation
-
Y.H. Du, Y. Lou, Qualitative behavior of positive solutions of a predator-prey model: effects of saturation, Proc. R. Soc. Edinburgh 131A (2001) 321-349.
-
(2001)
Proc. R. Soc. Edinburgh
, vol.131 A
, pp. 321-349
-
-
Du, Y.H.1
Lou, Y.2
-
10
-
-
0033785932
-
The effect of parasites on host population density and extinction: Experimental epidemiology with Daphnia and six microparasites
-
D. Ebert, M. Lipstich, K.L. Mangin, The effect of parasites on host population density and extinction: experimental epidemiology with Daphnia and six microparasites, Am. Nat. 156 (2000) 459-477.
-
(2000)
Am. Nat.
, vol.156
, pp. 459-477
-
-
Ebert, D.1
Lipstich, M.2
Mangin, K.L.3
-
11
-
-
0015454185
-
A theory of biological pattern formation
-
A. Gierer, H. Meinhardt, A theory of biological pattern formation, Kybernetik 12 (1972) 30-39.
-
(1972)
Kybernetik
, vol.12
, pp. 30-39
-
-
Gierer, A.1
Meinhardt, H.2
-
12
-
-
84990585735
-
Uniqueness and nonuniqueness of coexistence states in the Lotka-Volterra competition model
-
C.F. Gui, Y. Lou, Uniqueness and nonuniqueness of coexistence states in the Lotka-Volterra competition model, Comm. Pure Appl. Math. 47 (12) (1994) 1571-1594.
-
(1994)
Comm. Pure Appl. Math.
, vol.47
, Issue.12
, pp. 1571-1594
-
-
Gui, C.F.1
Lou, Y.2
-
13
-
-
0039978016
-
Geometric theory of semilinear parabolic equations
-
Springer-Verlag, Berlin, New York
-
D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin, New York, 1993.
-
(1993)
Lecture Notes in Mathematics
, vol.840
-
-
Henry, D.1
-
14
-
-
0037210844
-
A ratio-dependent food chain model and its applications to biological control
-
S.B. Hsu, T.W. Hwang, Y. Kuang, A ratio-dependent food chain model and its applications to biological control, Math. Biosci. 181 (2003) 55-83.
-
(2003)
Math. Biosci.
, vol.181
, pp. 55-83
-
-
Hsu, S.B.1
Hwang, T.W.2
Kuang, Y.3
-
15
-
-
0042760337
-
Deterministic extinction effect of parasites on host populations
-
T.W. Hwang, Y. Kuang, Deterministic extinction effect of parasites on host populations, J. Math. Biol. 46 (2003) 17-30.
-
(2003)
J. Math. Biol.
, vol.46
, pp. 17-30
-
-
Hwang, T.W.1
Kuang, Y.2
-
16
-
-
0002085758
-
An interfacial approach to regional segregation of two competing species mediated by a predator
-
T. Ikeda, M. Mimura, An interfacial approach to regional segregation of two competing species mediated by a predator, J. Math. Biol. 31 (1993) 215-240.
-
(1993)
J. Math. Biol.
, vol.31
, pp. 215-240
-
-
Ikeda, T.1
Mimura, M.2
-
17
-
-
0028371846
-
Pattern selection for two breathers
-
T. Ikeda, Y. Nishiura, Pattern selection for two breathers, SIAM J. Appl. Math. 54 (1) (1994) 195-230.
-
(1994)
SIAM J. Appl. Math.
, vol.54
, Issue.1
, pp. 195-230
-
-
Ikeda, T.1
Nishiura, Y.2
-
18
-
-
0035277877
-
The stability of spike solutions to the one-dimensional Gierer-Meinhardt model
-
D. Iron, M.J. Ward, J.C. Wei, The stability of spike solutions to the one-dimensional Gierer-Meinhardt model, Phys. D 150 (1/2) (2001) 25-62.
-
(2001)
Phys. D
, vol.150
, Issue.1-2
, pp. 25-62
-
-
Iron, D.1
Ward, M.J.2
Wei, J.C.3
-
19
-
-
0034652878
-
Existence and instability of Neumann layer solutions for a 3-component Lotka-Volterra model with diffusion
-
Y. Kan-on, Existence and instability of Neumann layer solutions for a 3-component Lotka-Volterra model with diffusion. J. Math. Anal. Appl. 243 (2000) 357-372.
-
(2000)
J. Math. Anal. Appl.
, vol.243
, pp. 357-372
-
-
Kan-On, Y.1
-
20
-
-
0032389543
-
Singular perturbation approach to a 3-component reaction-diffusion system arising in population dynamics
-
Y. Kan-on, M. Mimura, Singular perturbation approach to a 3-component reaction-diffusion system arising in population dynamics, SIAM J. Math. Anal. 29 (1998) 1519-1536.
-
(1998)
SIAM J. Math. Anal.
, vol.29
, pp. 1519-1536
-
-
Kan-On, Y.1
Mimura, M.2
-
21
-
-
0038823713
-
Pattern formation in a simple chemical system with general orders of autocatalysis and decay. I. Stability analysis
-
J.A. Leach, J.C. Wei, Pattern formation in a simple chemical system with general orders of autocatalysis and decay. I. Stability analysis, Phys. D 180 (3/4) (2003) 185-209.
-
(2003)
Phys. D
, vol.180
, Issue.3-4
, pp. 185-209
-
-
Leach, J.A.1
Wei, J.C.2
-
22
-
-
0002542873
-
Large amplitude stationary solutions to a chemotaxis systems
-
C.S. Lin, W.M. Ni, I. Takagi, Large amplitude stationary solutions to a chemotaxis systems, J. Differential Equations 72 (1988) 1-27.
-
(1988)
J. Differential Equations
, vol.72
, pp. 1-27
-
-
Lin, C.S.1
Ni, W.M.2
Takagi, I.3
-
23
-
-
0347055376
-
On 3 × 3 Lotka-Volterra competition systems with cross-diffusion
-
Y. Lou, S. Martinez, W.M. Ni, On 3 × 3 Lotka-Volterra competition systems with cross-diffusion, Discrete Contin. Dyn. Syst. 6 (1) (2000) 175-190.
-
(2000)
Discrete Contin. Dyn. Syst.
, vol.6
, Issue.1
, pp. 175-190
-
-
Lou, Y.1
Martinez, S.2
Ni, W.M.3
-
24
-
-
0030579038
-
Diffusion, self-diffusion and cross-diffusion
-
Y. Lou, W.M. Ni, Diffusion, self-diffusion and cross-diffusion, J. Differential Equations 131 (1996) 79-131.
-
(1996)
J. Differential Equations
, vol.131
, pp. 79-131
-
-
Lou, Y.1
Ni, W.M.2
-
25
-
-
0033130048
-
Diffusion vs. cross-diffusion: An elliptic approach
-
Y. Lou, W.M. Ni, Diffusion vs. cross-diffusion: an elliptic approach, J. Differential Equations 154 (1999) 157-190.
-
(1999)
J. Differential Equations
, vol.154
, pp. 157-190
-
-
Lou, Y.1
Ni, W.M.2
-
26
-
-
0008827179
-
Pattern formation in coupled reaction-diffusion systems
-
M. Mimura, Y. Nishiura, Pattern formation in coupled reaction-diffusion systems, Jpn. J. Indust. Appl. Math. 12 (3) (1995) 385-424.
-
(1995)
Jpn. J. Indust. Appl. Math.
, vol.12
, Issue.3
, pp. 385-424
-
-
Mimura, M.1
Nishiura, Y.2
-
27
-
-
0003002827
-
Diffusion, cross-diffusion and their spike-layer steady-states
-
W.M. Ni, Diffusion, cross-diffusion and their spike-layer steady-states, Notices Am. Math. Soc. 45 (1) (1998) 9-18.
-
(1998)
Notices Am. Math. Soc.
, vol.45
, Issue.1
, pp. 9-18
-
-
Ni, W.M.1
-
29
-
-
0041471616
-
Existence and stability of singular patterns in a Ginzburg-Landau equation coupled with a mean field
-
J. Norbury, J.C. Wei, M. Winter, Existence and stability of singular patterns in a Ginzburg-Landau equation coupled with a mean field, Nonlinearity 15 (6) (2002) 2077-2096.
-
(2002)
Nonlinearity
, vol.15
, Issue.6
, pp. 2077-2096
-
-
Norbury, J.1
Wei, J.C.2
Winter, M.3
-
30
-
-
1442279582
-
Non-constant positive steady states of a predator-prey system with non-monotonic functional response and diffusion
-
P.Y.H. Pang, M.X. Wang, Non-constant positive steady states of a predator-prey system with non-monotonic functional response and diffusion, Proc. Lond. Math. Soc. 88 (1) (2004) 135-157.
-
(2004)
Proc. Lond. Math. Soc.
, vol.88
, Issue.1
, pp. 135-157
-
-
Pang, P.Y.H.1
Wang, M.X.2
-
31
-
-
0141957171
-
Qualitative analysis of a ratio-dependent predator-prey system with diffusion
-
P.Y.H. Pang, M.X. Wang, Qualitative analysis of a ratio-dependent predator-prey system with diffusion, Proc. R. Soc. Edinburgh A 133 (4) (2003) 919-942.
-
(2003)
Proc. R. Soc. Edinburgh A
, vol.133
, Issue.4
, pp. 919-942
-
-
Pang, P.Y.H.1
Wang, M.X.2
-
32
-
-
0346340796
-
Positive steady-state solutions of the Noyes-Field model for Belousov-Zhabotinskii reaction
-
R. Peng, M.X. Wang, Positive steady-state solutions of the Noyes-Field model for Belousov-Zhabotinskii reaction, Nonlinear Anal. TMA 56 (2004) 451-464.
-
(2004)
Nonlinear Anal. TMA
, vol.56
, pp. 451-464
-
-
Peng, R.1
Wang, M.X.2
-
33
-
-
0001739076
-
Positive steady-state solutions of a competing reaction-diffusion system
-
W.H. Ruan, C.V. Pao, Positive steady-state solutions of a competing reaction-diffusion system, J. Differential Equations 117 (1995) 411-427.
-
(1995)
J. Differential Equations
, vol.117
, pp. 411-427
-
-
Ruan, W.H.1
Pao, C.V.2
-
34
-
-
0002011401
-
The chemical basis of morphogenesis
-
A. Turing, The chemical basis of morphogenesis, Philos. Trans. R. Soc. B 237 (1952) 37-72.
-
(1952)
Philos. Trans. R. Soc. B
, vol.237
, pp. 37-72
-
-
Turing, A.1
-
35
-
-
0037845132
-
Non-constant positive steady states of the Sel'kov model
-
M.X. Wang, Non-constant positive steady states of the Sel'kov model, J. Differential Equations 190 (2) (2003) 600-620.
-
(2003)
J. Differential Equations
, vol.190
, Issue.2
, pp. 600-620
-
-
Wang, M.X.1
-
36
-
-
1942508094
-
Stationary patterns of strongly coupled predator-prey models
-
M.X. Wang, Stationary patterns of strongly coupled predator-prey models, J. Math. Anal. Appl. 292 (2) (2004) 484-505.
-
(2004)
J. Math. Anal. Appl.
, vol.292
, Issue.2
, pp. 484-505
-
-
Wang, M.X.1
-
37
-
-
0036677909
-
Qualitative analysis on a chemotactic diffusion model for two species competing for a limited resource
-
X.F. Wang, Y.P. Wu, Qualitative analysis on a chemotactic diffusion model for two species competing for a limited resource, Q. Appl. Math. LX (3) (2002) 505-531.
-
(2002)
Q. Appl. Math.
, vol.60
, Issue.3
, pp. 505-531
-
-
Wang, X.F.1
Wu, Y.P.2
-
38
-
-
0037137989
-
Spikes for the Gierer-Meinhardt system in two dimensions: The strong coupling case
-
J.C. Wei, M. Winter, Spikes for the Gierer-Meinhardt system in two dimensions: the strong coupling case, J. Differential Equations 178 (2) (2002) 478-518.
-
(2002)
J. Differential Equations
, vol.178
, Issue.2
, pp. 478-518
-
-
Wei, J.C.1
Winter, M.2
-
40
-
-
0036977415
-
Existence of stationary solutions with transition layers for a class of cross-diffusion systems
-
Y.P. Wu, Existence of stationary solutions with transition layers for a class of cross-diffusion systems, Proc. R. Soc. Edinburgh 132A (2002) 1493-1511.
-
(2002)
Proc. R. Soc. Edinburgh
, vol.132 A
, pp. 1493-1511
-
-
Wu, Y.P.1
-
41
-
-
0037050701
-
Mini-maximizer for reaction-diffusion systems with skew-gradient structure
-
E. Yanagida, Mini-maximizer for reaction-diffusion systems with skew-gradient structure, J. Differential Equations 179 (1) (2002) 311-335.
-
(2002)
J. Differential Equations
, vol.179
, Issue.1
, pp. 311-335
-
-
Yanagida, E.1
|