-
1
-
-
0034255819
-
The nature of predation: Prey dependent, ratio dependent or neither?
-
P. ABRAMS AND L. GINZBURG, The nature of predation: Prey dependent, ratio dependent or neither?, Trends Ecol. Evol., 15 (2000), pp. 337-341.
-
(2000)
Trends Ecol. Evol
, vol.15
, pp. 337-341
-
-
ABRAMS, P.1
GINZBURG, L.2
-
2
-
-
0036141801
-
Mutual interference between predators can give rise to Turing spatial patterns
-
D. ALONSO, F. BARTUMEUS, AND J. CATALAN, Mutual interference between predators can give rise to Turing spatial patterns, Ecology, 83 (2002), pp. 28-34.
-
(2002)
Ecology
, vol.83
, pp. 28-34
-
-
ALONSO, D.1
BARTUMEUS, F.2
CATALAN, J.3
-
3
-
-
0038778726
-
Global bifurcation in the Brusselator system
-
K. J, BROWN AND F. A. DAVIDSON, Global bifurcation in the Brusselator system, Nonlinear Anal., 24 (1995), pp. 1713-1725.
-
(1995)
Nonlinear Anal
, vol.24
, pp. 1713-1725
-
-
BROWN, K.J.1
DAVIDSON, F.A.2
-
4
-
-
0346072299
-
Pattern formation in three-dimensional reaction-diffusion systems
-
T. K. CALLAHAN AND E. KNOBLOCH, Pattern formation in three-dimensional reaction-diffusion systems, Phys. D, 132 (1999), pp. 339-362.
-
(1999)
Phys. D
, vol.132
, pp. 339-362
-
-
CALLAHAN, T.K.1
KNOBLOCH, E.2
-
5
-
-
0000013771
-
Extinction of top predator in a three-level food-chain model
-
C. H. CHIU AND S. B. HSU, Extinction of top predator in a three-level food-chain model, J. Math. Biol., 37 (1998), pp. 372-380.
-
(1998)
J. Math. Biol
, vol.37
, pp. 372-380
-
-
CHIU, C.H.1
HSU, S.B.2
-
6
-
-
0001842649
-
Large time behavior of solutions of systems of nonlinear reaction-diffusion equations
-
E. CONWAY, D. HOFF, AND J. SMOLLER, Large time behavior of solutions of systems of nonlinear reaction-diffusion equations, SIAM J. Appl. Math., 35 (1978), pp. 1-16.
-
(1978)
SIAM J. Appl. Math
, vol.35
, pp. 1-16
-
-
CONWAY, E.1
HOFF, D.2
SMOLLER, J.3
-
7
-
-
23044517800
-
A priori bounds and global existence of solutions of the steady-state Sel'kov model
-
F. A. DAVIDSON AND B, P. RYNNE, A priori bounds and global existence of solutions of the steady-state Sel'kov model, Proc. Roy. Soc. Edinburgh Sect. A, 130 (2000), pp. 507-516.
-
(2000)
Proc. Roy. Soc. Edinburgh Sect. A
, vol.130
, pp. 507-516
-
-
DAVIDSON, F.A.1
RYNNE, B.P.2
-
8
-
-
23044527512
-
Qualitative behavior of positive solutions of a predator-prey model: Effects of saturation
-
Y. H. DU AND Y. LOU, Qualitative behavior of positive solutions of a predator-prey model: Effects of saturation, Proc. Roy. Soc. Edinburgh Sect. A, 131 (2001), pp. 321-349.
-
(2001)
Proc. Roy. Soc. Edinburgh Sect. A
, vol.131
, pp. 321-349
-
-
DU, Y.H.1
LOU, Y.2
-
9
-
-
0017407813
-
Mathematical analysis of some three-species food-chain models
-
H. I. FREEDMAN AND P. WALTMAN, Mathematical analysis of some three-species food-chain models, Math. Biosci., 33 (1977), pp. 257-277.
-
(1977)
Math. Biosci
, vol.33
, pp. 257-277
-
-
FREEDMAN, H.I.1
WALTMAN, P.2
-
10
-
-
0019405577
-
Generation of biological patterns and form: Some physical, mathematical and logical aspects
-
A. GIERER, Generation of biological patterns and form: Some physical, mathematical and logical aspects, Prog. Biophys. Biol., 37 (1981), pp. 1-47.
-
(1981)
Prog. Biophys. Biol
, vol.37
, pp. 1-47
-
-
GIERER, A.1
-
11
-
-
0025956240
-
Chaos in a three-species food chain
-
A. HASTINGS, T, POWELL, AND S. B. HSU, Chaos in a three-species food chain, Ecology, 72 (1991), pp. 896-903.
-
(1991)
Ecology
, vol.72
, pp. 896-903
-
-
HASTINGS, A.1
POWELL, T.2
HSU, S.B.3
-
12
-
-
0039978016
-
Geometric Theory of Semilinear Parabolic Equations
-
Springer-Verlag, Berlin, New York
-
D. HENRY, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math. 840, Springer-Verlag, Berlin, New York, 1993.
-
(1993)
Lecture Notes in Math
, vol.840
-
-
HENRY, D.1
-
13
-
-
0037210844
-
A ratio-dependent food chain model and its applications to biological control
-
S. B. HSU, T. W. HWANG, AND Y. KUANG, A ratio-dependent food chain model and its applications to biological control, Math. Biosci., 181 (2003), pp. 55-83.
-
(2003)
Math. Biosci
, vol.181
, pp. 55-83
-
-
HSU, S.B.1
HWANG, T.W.2
KUANG, Y.3
-
14
-
-
21444453892
-
Competitive exclusion and coexistence for competitive systems on ordered Banach spaces
-
S. B. HSU, H. L. SMITH, AND P. WALTMAN, Competitive exclusion and coexistence for competitive systems on ordered Banach spaces, Trans. Amer. Math. Soc., 348 (1996), pp. 4083-4094.
-
(1996)
Trans. Amer. Math. Soc
, vol.348
, pp. 4083-4094
-
-
HSU, S.B.1
SMITH, H.L.2
WALTMAN, P.3
-
15
-
-
0034652878
-
Existence and instability of Neumann layer solutions for a Z-component Lotka Volterra model with diffusion
-
Y. KAN-ON, Existence and instability of Neumann layer solutions for a Z-component Lotka Volterra model with diffusion, J. Math. Anal. Appl., 243 (2000), pp. 357-372.
-
(2000)
J. Math. Anal. Appl
, vol.243
, pp. 357-372
-
-
KAN-ON, Y.1
-
16
-
-
0032389543
-
Singular perturbation approach to a 3-component reactiondiffusion system arising in population dynamics
-
Y. KAN-ON AND M. MLMURA, Singular perturbation approach to a 3-component reactiondiffusion system arising in population dynamics, SIAM J. Math. Anal., 29 (1998), pp. 1519-1536.
-
(1998)
SIAM J. Math. Anal
, vol.29
, pp. 1519-1536
-
-
KAN-ON, Y.1
MLMURA, M.2
-
17
-
-
0028161492
-
Chaos in one-predator, two-prey models: General results from bifurcation theory
-
A. KLEBANOFF AND A. HASTINGS, Chaos in one-predator, two-prey models: General results from bifurcation theory, Math. Biosci., 122 (1994), pp. 221-233.
-
(1994)
Math. Biosci
, vol.122
, pp. 221-233
-
-
KLEBANOFF, A.1
HASTINGS, A.2
-
18
-
-
0038823713
-
Pattern formation in a simple chemical system with general orders of autocatalysis and decay. I. Stability analysis
-
J. A. LEACH AND J. C. WEI, Pattern formation in a simple chemical system with general orders of autocatalysis and decay. I. Stability analysis, Phys. D, 180 (2003), pp. 185-209.
-
(2003)
Phys. D
, vol.180
, pp. 185-209
-
-
LEACH, J.A.1
WEI, J.C.2
-
19
-
-
0002542873
-
Large amplitude stationary solutions to a Chemotaxis system
-
C. S. LIN, W. M. NI, AND I. TAKAGI, Large amplitude stationary solutions to a Chemotaxis system, J. Differential Equations, 72 (1988), pp. 1-27.
-
(1988)
J. Differential Equations
, vol.72
, pp. 1-27
-
-
LIN, C.S.1
NI, W.M.2
TAKAGI, I.3
-
20
-
-
0347055376
-
On 3 × 3 Lotka-Volterra competition systems with cross-diffusion
-
Y. LOU, S. MARTINEZ, AND W. M. NI, On 3 × 3 Lotka-Volterra competition systems with cross-diffusion, Discrete Contin. Dyn. Syst., 6 (2000), pp. 175-190.
-
(2000)
Discrete Contin. Dyn. Syst
, vol.6
, pp. 175-190
-
-
LOU, Y.1
MARTINEZ, S.2
NI, W.M.3
-
21
-
-
0033130048
-
Diffusion vs cross-diffusion: An elliptic approach
-
Y. LOU AND W. M. NI, Diffusion vs cross-diffusion: An elliptic approach, J. Differential Equations, 154 (1999), pp. 157-190.
-
(1999)
J. Differential Equations
, vol.154
, pp. 157-190
-
-
LOU, Y.1
NI, W.M.2
-
22
-
-
0008827179
-
Pattern formation in coupled reaction-diffusion systems
-
M. MIMURA AND Y. NISHIURA, Pattern formation in coupled reaction-diffusion systems, Japan J. Indust. Appl. Math., 12 (1995), pp. 385-424.
-
(1995)
Japan J. Indust. Appl. Math
, vol.12
, pp. 385-424
-
-
MIMURA, M.1
NISHIURA, Y.2
-
23
-
-
0001548639
-
On the Neumann problem for some semilinear elliptic equations and systems of activator-inhibitor type
-
W. M. NI AND I. TAKAGI, On the Neumann problem for some semilinear elliptic equations and systems of activator-inhibitor type, Trans. Amer. Math. Soc., 297 (1986), pp. 351-368.
-
(1986)
Trans. Amer. Math. Soc
, vol.297
, pp. 351-368
-
-
NI, W.M.1
TAKAGI, I.2
-
24
-
-
30344464119
-
On positive solutions concentrating on spheres for the Gierer-Meinhardt system
-
W. M. NI AND J. C. WEI, On positive solutions concentrating on spheres for the Gierer-Meinhardt system, J. Differential Equations, 221 (2006), pp. 158-189.
-
(2006)
J. Differential Equations
, vol.221
, pp. 158-189
-
-
NI, W.M.1
WEI, J.C.2
-
26
-
-
0037671486
-
Pattern formation in spatially heterogeneous Turing reaction-diffusion models
-
K. PAGE, P. K. MAINI, AND N. A. M. MONK, Pattern formation in spatially heterogeneous Turing reaction-diffusion models, Phys. D, 181 (2003), pp. 80-101.
-
(2003)
Phys. D
, vol.181
, pp. 80-101
-
-
PAGE, K.1
MAINI, P.K.2
MONK, N.A.M.3
-
27
-
-
1442279582
-
Non-constant positive steady states of a predator-prey system with non-monotonic functional response and diffusion
-
P. Y. H. PANG AND M. X. WANG, Non-constant positive steady states of a predator-prey system with non-monotonic functional response and diffusion, Proc London Math. Soc. (3), 88 (2004), pp. 135-157.
-
(2004)
Proc London Math. Soc
, vol.88
, Issue.3
, pp. 135-157
-
-
PANG, P.Y.H.1
WANG, M.X.2
-
28
-
-
0141957171
-
Qualitative analysis of a ratio-dependent predator-prey system with diffusion
-
P. Y. H. PANG AND M. X. WANG, Qualitative analysis of a ratio-dependent predator-prey system with diffusion, Proc. Roy. Soc. Edinburgh Sect. A, 133 (2003), pp. 919-942.
-
(2003)
Proc. Roy. Soc. Edinburgh Sect. A
, vol.133
, pp. 919-942
-
-
PANG, P.Y.H.1
WANG, M.X.2
-
29
-
-
0346340796
-
Positive steady-state solutions of the Noyes-Field model for Belousov-Zhabotinskii reaction
-
R. PENG AND M. X. WANG, Positive steady-state solutions of the Noyes-Field model for Belousov-Zhabotinskii reaction, Nonlinear Anal., 56 (2004), pp. 451-464.
-
(2004)
Nonlinear Anal
, vol.56
, pp. 451-464
-
-
PENG, R.1
WANG, M.X.2
-
30
-
-
22144487744
-
Pattern formation in the Brusselator system
-
R. PENG AND M. X. WANG, Pattern formation in the Brusselator system, J. Math. Anal. Appl., 309 (2005), pp. 151-166.
-
(2005)
J. Math. Anal. Appl
, vol.309
, pp. 151-166
-
-
PENG, R.1
WANG, M.X.2
-
31
-
-
14644406942
-
Positive steady-states of the Holling-Tanner prey-predator model with diffusion
-
R. PENG AND M. X. WANG, Positive steady-states of the Holling-Tanner prey-predator model with diffusion, Proc. Roy. Soc. Edinburgh Sect. A, 135 (2005), pp. 149-164.
-
(2005)
Proc. Roy. Soc. Edinburgh Sect. A
, vol.135
, pp. 149-164
-
-
PENG, R.1
WANG, M.X.2
-
32
-
-
34547176335
-
On pattern formation in the Gray-Scott model
-
R. PENG AND M. X. WANG, On pattern formation in the Gray-Scott model, Sci. China Ser. A, 50 (2007), pp. 377-386.
-
(2007)
Sci. China Ser. A
, vol.50
, pp. 377-386
-
-
PENG, R.1
WANG, M.X.2
-
33
-
-
0015243940
-
Paradox of enrichment: Destabilization of exploitation systems in ecological time
-
M. L. ROSENZWEIG, Paradox of enrichment: Destabilization of exploitation systems in ecological time, Science, 171 (1969), pp. 385-387.
-
(1969)
Science
, vol.171
, pp. 385-387
-
-
ROSENZWEIG, M.L.1
-
34
-
-
0002011401
-
The chemical basis of morphogenesis
-
A. TURING, The chemical basis of morphogenesis, Philos. Trans. R. Soc. Lond. Ser. B., 237 (1952), pp. 37-72.
-
(1952)
Philos. Trans. R. Soc. Lond. Ser. 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 (2003), pp. 600-620.
-
(2003)
J. Differential Equations
, vol.190
, pp. 600-620
-
-
WANG, M.X.1
-
36
-
-
3242888035
-
Stationary patterns for a prey-predator model with prey-dependent and ratio-dependent functional responses and diffusion
-
M. X. WANG, Stationary patterns for a prey-predator model with prey-dependent and ratio-dependent functional responses and diffusion, Phys. D, 196 (2004), pp. 172-192.
-
(2004)
Phys. D
, vol.196
, pp. 172-192
-
-
WANG, M.X.1
-
37
-
-
0037367343
-
Existence and stability of multiple-spot solutions for the Gray-Scott model in R2
-
J. C. WEI AND M. WINTER, Existence and stability of multiple-spot solutions for the Gray-Scott model in R2, Phys. D, 176 (2003), pp. 147-180.
-
(2003)
Phys. D
, vol.176
, pp. 147-180
-
-
WEI, J.C.1
WINTER, M.2
|