-
2
-
-
0028443125
-
Algorithm 731: A moving-grid interface for systems of one-dimensional time-dependent partial differential equations
-
Blom J.G., Zegeling P.A., Algorithm 731: a moving-grid interface for systems of one-dimensional time-dependent partial differential equations. Assoc. Comput. Mach. Trans. Math. Software. 20:1994;194-214.
-
(1994)
Assoc. Comput. Mach. Trans. Math. Software
, vol.20
, pp. 194-214
-
-
Blom, J.G.1
Zegeling, P.A.2
-
3
-
-
36149044710
-
Nonlinear properties of thermal convection
-
Busse F.H., Nonlinear properties of thermal convection. Rep. Prog. Phys. 41:1978;1929-1967.
-
(1978)
Rep. Prog. Phys.
, vol.41
, pp. 1929-1967
-
-
Busse, F.H.1
-
4
-
-
0022692326
-
The interior transition layer for an ordinary differential equation arising from solidification theory
-
Caginalp G., McLeod B., The interior transition layer for an ordinary differential equation arising from solidification theory. Quart. Appl. Math. 44:1986;155-168.
-
(1986)
Quart. Appl. Math.
, vol.44
, pp. 155-168
-
-
Caginalp, G.1
McLeod, B.2
-
5
-
-
0000550494
-
Dividing blobs, chemical flowers, and patterned islands in a reaction-diffusion system
-
Davies P., Blanchedeau P., Dulos E., Kepper P.D., Dividing blobs, chemical flowers, and patterned islands in a reaction-diffusion system. J. Phys. Chem. 102:1998;8236-8244.
-
(1998)
J. Phys. Chem.
, vol.102
, pp. 8236-8244
-
-
Davies, P.1
Blanchedeau, P.2
Dulos, E.3
Kepper, P.D.4
-
6
-
-
0034912344
-
Slowly-modulated two-pulse solutions in the Gray-Scott model. I. Asymptotic construction and stability
-
Doelman A., Eckhaus W., Kaper T.J., Slowly-modulated two-pulse solutions in the Gray-Scott model. I. Asymptotic construction and stability. SIAM J. Appl. Math. 61:2001;1080-1102.
-
(2001)
SIAM J. Appl. Math.
, vol.61
, pp. 1080-1102
-
-
Doelman, A.1
Eckhaus, W.2
Kaper, T.J.3
-
7
-
-
0035704463
-
Slowly-modulated two-pulse solutions in the Gray-Scott model. II. Geometric theory, bifurcations, and splitting dynamics
-
Doelman A., Eckhaus W., Kaper T.J., Slowly-modulated two-pulse solutions in the Gray-Scott model. II. Geometric theory, bifurcations, and splitting dynamics. SIAM J. Appl. Math. 61:2001;2036-2062.
-
(2001)
SIAM J. Appl. Math.
, vol.61
, pp. 2036-2062
-
-
Doelman, A.1
Eckhaus, W.2
Kaper, T.J.3
-
8
-
-
0005468518
-
Stability analysis of singular patterns in the 1D Gray-Scott model: A matched asymptotics approach
-
Doelman A., Gardner R.A., Kaper T.J., Stability analysis of singular patterns in the 1D Gray-Scott model: a matched asymptotics approach. Physica D. 122:1998;1-36.
-
(1998)
Physica D
, vol.122
, pp. 1-36
-
-
Doelman, A.1
Gardner, R.A.2
Kaper, T.J.3
-
9
-
-
0000132086
-
Large stable pulse solutions in reaction-diffusion equations
-
Doelman A., Gardner R.A., Kaper T.J., Large stable pulse solutions in reaction-diffusion equations. Indiana Univ. Math. J. 50:2001;443-507.
-
(2001)
Indiana Univ. Math. J.
, vol.50
, pp. 443-507
-
-
Doelman, A.1
Gardner, R.A.2
Kaper, T.J.3
-
10
-
-
85087535076
-
A stability index analysis of 1D patterns of the Gray-Scott model
-
AMS, Providence, RI. ISSN 0065-9266
-
A. Doelman, R.A. Gardner, T.J. Kaper, A stability index analysis of 1D patterns of the Gray-Scott model, Mem. Am. Math. Soc. 155 (737) (2002), AMS, Providence, RI. ISSN 0065-9266.
-
(2002)
Mem. Am. Math. Soc.
, vol.155
, Issue.737
-
-
Doelman, A.1
Gardner, R.A.2
Kaper, T.J.3
-
11
-
-
1842839666
-
Semi-strong pulse interactions in a class of coupled reaction-diffusion equations
-
Doelman A., Kaper T.J., Semi-strong pulse interactions in a class of coupled reaction-diffusion equations. SIAM J. Appl. Dyn. Syst. 2:2003;53-96.
-
(2003)
SIAM J. Appl. Dyn. Syst.
, vol.2
, pp. 53-96
-
-
Doelman, A.1
Kaper, T.J.2
-
12
-
-
0000706319
-
Pattern formation in the one-dimensional Gray-Scott model
-
Doelman A., Kaper T.J., Zegeling P., Pattern formation in the one-dimensional Gray-Scott model. Nonlinearity. 10:1997;523-563.
-
(1997)
Nonlinearity
, vol.10
, pp. 523-563
-
-
Doelman, A.1
Kaper, T.J.2
Zegeling, P.3
-
17
-
-
0020607165
-
Autocatalytic reactions in the isothermal, continuous stirred tank reactor: Isolas and other forms of multistability
-
Gray P., Scott S.K., Autocatalytic reactions in the isothermal, continuous stirred tank reactor: isolas and other forms of multistability. Chem. Eng. Sci. 38:1983;29-43.
-
(1983)
Chem. Eng. Sci.
, vol.38
, pp. 29-43
-
-
Gray, P.1
Scott, S.K.2
-
18
-
-
0021310291
-
Autocatalytic reactions in the isothermal, continuous stirred tank reactor: Oscillations and instabilities in the system A+2B→3B , B→C
-
Gray P., Scott S.K., Autocatalytic reactions in the isothermal, continuous stirred tank reactor: oscillations and instabilities in the system. A+2B→3B, B→C Chem. Eng. Sci. 39:1984;1087-1097.
-
(1984)
Chem. Eng. Sci.
, vol.39
, pp. 1087-1097
-
-
Gray, P.1
Scott, S.K.2
-
19
-
-
0034207069
-
Phase dynamics of nearly stationary patterns in activator-inhibitor systems
-
Hagberg A., Meron E., Passot T., Phase dynamics of nearly stationary patterns in activator-inhibitor systems. Phys. Rev. E. 61:2000;6471-6476.
-
(2000)
Phys. Rev. E
, vol.61
, pp. 6471-6476
-
-
Hagberg, A.1
Meron, E.2
Passot, T.3
-
20
-
-
0001158137
-
Breathing spots in a reaction-diffusion system
-
Haim D., Li G., Ouyang Q., McCormick W.D., Swinney H., Hagberg A., Meron E., Breathing spots in a reaction-diffusion system. Phys. Rev. Lett. 77:1996;190.
-
(1996)
Phys. Rev. Lett.
, vol.77
, pp. 190
-
-
Haim, D.1
Li, G.2
Ouyang, Q.3
McCormick, W.D.4
Swinney, H.5
Hagberg, A.6
Meron, E.7
-
21
-
-
0007987708
-
Zigzag and varicose instabilities of a localized stripe
-
Hirschberg P., Knobloch E., Zigzag and varicose instabilities of a localized stripe. Chaos. 3:1993;713-721.
-
(1993)
Chaos
, vol.3
, pp. 713-721
-
-
Hirschberg, P.1
Knobloch, E.2
-
22
-
-
0037446124
-
Two-bump solutions of Amari-type models of neuronal pattern formation
-
Laing C., Troy W., Two-bump solutions of Amari-type models of neuronal pattern formation. Physica D. 178:2003;190-218.
-
(2003)
Physica D
, vol.178
, pp. 190-218
-
-
Laing, C.1
Troy, W.2
-
23
-
-
35949006727
-
Lamellar structures and self-replicating spots in a reaction-diffusion system
-
Lee K.J., Swinney H.L., Lamellar structures and self-replicating spots in a reaction-diffusion system. Phys. Rev. E. 51:1995;1899-1915.
-
(1995)
Phys. Rev. E
, vol.51
, pp. 1899-1915
-
-
Lee, K.J.1
Swinney, H.L.2
-
24
-
-
0011699805
-
Replicating spots in reaction-diffusion systems
-
Lee K., Swinney H., Replicating spots in reaction-diffusion systems. Int. J. Bifurcat. Chaos. 7:1995;1149-1158.
-
(1995)
Int. J. Bifurcat. Chaos
, vol.7
, pp. 1149-1158
-
-
Lee, K.1
Swinney, H.2
-
25
-
-
0028242433
-
Experimental observation of self-replicating spots in a reaction-diffusion system
-
Lin K.-J., McCormick W.D., Pearson J.E., Swinney H.L., Experimental observation of self-replicating spots in a reaction-diffusion system. Nature. 369(6477):1994;215-218.
-
(1994)
Nature
, vol.369
, Issue.6477
, pp. 215-218
-
-
Lin, K.-J.1
McCormick, W.D.2
Pearson, J.E.3
Swinney, H.L.4
-
26
-
-
0001622202
-
Nonannihilation dynamics in an exothermic reaction-diffusion system with mono-stable excitability
-
Mimura M., Nagayama M., Nonannihilation dynamics in an exothermic reaction-diffusion system with mono-stable excitability. Chaos. 7:1997;817-826.
-
(1997)
Chaos
, vol.7
, pp. 817-826
-
-
Mimura, M.1
Nagayama, M.2
-
27
-
-
0000545006
-
Stationary periodic orbits in the 1D Gray-Scott model
-
Morgan D.S., Doelman A., Kaper T.J., Stationary periodic orbits in the 1D Gray-Scott model. Meth. Appl. Anal. 7:2000;105-150.
-
(2000)
Meth. Appl. Anal.
, vol.7
, pp. 105-150
-
-
Morgan, D.S.1
Doelman, A.2
Kaper, T.J.3
-
30
-
-
0034623753
-
Static spike autosolitons in the Gray-Scott model
-
Muratov C., Osipov V., Static spike autosolitons in the Gray-Scott model. J. Phys. A. 33:2000;8893-8916.
-
(2000)
J. Phys. A
, vol.33
, pp. 8893-8916
-
-
Muratov, C.1
Osipov, V.2
-
31
-
-
0036588860
-
Stability of the static spike autosolitons in the Gray-Scott model
-
Muratov C., Osipov V., Stability of the static spike autosolitons in the Gray-Scott model. SIAM J. Appl. Math. 62:2002;1463-1487.
-
(2002)
SIAM J. Appl. Math.
, vol.62
, pp. 1463-1487
-
-
Muratov, C.1
Osipov, V.2
-
32
-
-
0039981220
-
Contrast structures of spike type in nonlinear singularly perturbed elliptic equations
-
Nefedov N., Contrast structures of spike type in nonlinear singularly perturbed elliptic equations. Russ. Acad. Sci. Doklady Math. 46:1993;411-413.
-
(1993)
Russ. Acad. Sci. Doklady Math.
, vol.46
, pp. 411-413
-
-
Nefedov, N.1
-
33
-
-
0000988067
-
Stability of singularly perturbed solutions to systems of reaction-diffusion equations
-
Nishiura Y., Fujii H., Stability of singularly perturbed solutions to systems of reaction-diffusion equations. SIAM J. Math. Anal. 18:1987;1726-1770.
-
(1987)
SIAM J. Math. Anal.
, vol.18
, pp. 1726-1770
-
-
Nishiura, Y.1
Fujii, H.2
-
34
-
-
0032339678
-
Nonexistence of higher dimensional stable Turing patterns in the singular limit
-
Nishiura Y., Suzuki H., Nonexistence of higher dimensional stable Turing patterns in the singular limit. SIAM J. Math. Anal. 29:1998;1087-1105.
-
(1998)
SIAM J. Math. Anal.
, vol.29
, pp. 1087-1105
-
-
Nishiura, Y.1
Suzuki, H.2
-
35
-
-
0347038753
-
A skeleton structure for self-replication dynamics
-
Nishiura Y., Ueyama D., A skeleton structure for self-replication dynamics. Physica D. 130:1999;73-104.
-
(1999)
Physica D
, vol.130
, pp. 73-104
-
-
Nishiura, Y.1
Ueyama, D.2
-
36
-
-
0035311814
-
Spatio-temporal chaos for the Gray-Scott model
-
Nishiura Y., Ueyama D., Spatio-temporal chaos for the Gray-Scott model. Physica D. 150:2001;137-162.
-
(2001)
Physica D
, vol.150
, pp. 137-162
-
-
Nishiura, Y.1
Ueyama, D.2
-
37
-
-
0001102631
-
Complex patterns in a simple system
-
Pearson J.E., Complex patterns in a simple system. Science. 261:1993;189-192.
-
(1993)
Science
, vol.261
, pp. 189-192
-
-
Pearson, J.E.1
-
38
-
-
0030101235
-
Excitability, wave reflection, and wave splitting in a cubic autocatalysis reaction-diffusion system
-
Petrov V., Scott S.K., Showalter K., Excitability, wave reflection, and wave splitting in a cubic autocatalysis reaction-diffusion system. Phil. Trans. Roy. Soc. London, Ser. A. 347:1994;631-642.
-
(1994)
Phil. Trans. Roy. Soc. London, Ser. A
, vol.347
, pp. 631-642
-
-
Petrov, V.1
Scott, S.K.2
Showalter, K.3
-
39
-
-
1842839667
-
-
Personal communication
-
H.V.D. Ploeg, Personal communication.
-
-
-
Ploeg, H.V.D.1
-
40
-
-
0001360757
-
Dynamics of self-replicating patterns in reaction diffusion systems
-
Reynolds W.N., Pearson J.E., Ponce-Dawson S., Dynamics of self-replicating patterns in reaction diffusion systems. Phys. Rev. Lett. 72:1994;2797-2800.
-
(1994)
Phys. Rev. Lett.
, vol.72
, pp. 2797-2800
-
-
Reynolds, W.N.1
Pearson, J.E.2
Ponce-Dawson, S.3
-
43
-
-
0003663060
-
-
Springer-Verlag, New York
-
D. Walgraef, Spatio-temporal Pattern Formation: With Examples from Physics, Chemistry, and Materials Science, Springer-Verlag, New York, 1997.
-
(1997)
Spatio-temporal Pattern Formation: With Examples from Physics, Chemistry, and Materials Science
-
-
Walgraef, D.1
-
44
-
-
0003077491
-
Pattern formation in two-dimensional Gray-Scott model: Existence of single-spot solutions and their stability
-
Wei J., Pattern formation in two-dimensional Gray-Scott model: existence of single-spot solutions and their stability. Physica D. 148:2001;20-48.
-
(2001)
Physica D
, vol.148
, pp. 20-48
-
-
Wei, J.1
|