-
1
-
-
84968466504
-
Collocation software for boundary value ODE's
-
U. Ascher, R. Christiansen, R. Russell, Collocation Software for Boundary Value ODE's, Math. Comp., 33, (1979), pp. 659-679.
-
(1979)
Math. Comp.
, vol.33
, pp. 659-679
-
-
Ascher, U.1
Christiansen, R.2
Russell, R.3
-
2
-
-
12044252828
-
Pattern formation outside of equilibrium
-
M. Cross, P. Hohenburg, Pattern Formation Outside of Equilibrium, Rev. Mod. Phys., 65, (1993), pp. 851-1112.
-
(1993)
Rev. Mod. Phys.
, vol.65
, pp. 851-1112
-
-
Cross, M.1
Hohenburg, P.2
-
3
-
-
0013238621
-
On Stability and Hopf Bifurcations for Chemotaxis Systems
-
E. N. Dancer, On Stability and Hopf Bifurcations for Chemotaxis Systems, Meth. Appl. Anal., 8(2), (2001), pp. 245-256. (Pubitemid 36289753)
-
(2001)
Methods and Applications of Analysis
, vol.8
, Issue.2
, pp. 245-256
-
-
Dancer, E.N.1
-
4
-
-
0000706319
-
Pattern formation in the one-dimensional Gray-Scott model
-
PII S0951771597775662
-
A. Doelman, T. J. Kaper, P. Zegeling, Pattern Formation in the One-Dimensional Gray-Scott Model, Nonlinearity, 10, (1997), pp. 523-563. (Pubitemid 127430235)
-
(1997)
Nonlinearity
, vol.10
, Issue.2
, pp. 523-563
-
-
Doelman, A.1
Kaper, T.J.2
Zegeling, P.A.3
-
5
-
-
0011517497
-
Spatially Periodic and Aperiodic Multi-pulse Patterns in the One-dimensional Gierer-Meinhardt Equation
-
A. Doelman, T. Kaper, H. van der Ploeg, Spatially Periodic and Aperiodic Multi-Pulse Patterns in the One-Dimensional Gierer-Meinhardt Model, Meth. Appl. Anal., 8(3), (2001), pp. 387-414. (Pubitemid 36299751)
-
(2001)
Methods and Applications of Analysis
, vol.8
, Issue.3
, pp. 387-414
-
-
Doelman, A.1
Kaper, T.J.2
Van Der Ploeg, H.3
-
6
-
-
0005468518
-
Stability analysis of singular patterns in the 1D Gray-Scott model: A matched asymptotics approach
-
PII S0167278998001808
-
A. Doelman, R. A. Gardner, T. J. Kaper, Stability Analysis of Singular Patterns in the 1-D Gray-Scott Model: A Matched Asymptotics Approach, Physica D, 122, (1998), pp. 1-36. (Pubitemid 128636761)
-
(1998)
Physica D: Nonlinear Phenomena
, vol.122
, Issue.1-4
, pp. 1-36
-
-
Doelman, A.1
Gardner, R.A.2
Kaper, T.J.3
-
7
-
-
85087535076
-
A stability index analysis of 1-D patterns of the gray scott model
-
A. Doelman, R. A. Gardner, T. Kaper, A Stability Index Analysis of 1-D Patterns of the Gray Scott Model, Mem. AMS, 155, no. 737, (2002).
-
(2002)
Mem. AMS
, vol.155
, Issue.737
-
-
Doelman, A.1
Gardner, R.A.2
Kaper, T.3
-
8
-
-
0000132086
-
Large stable pulse solutions in reaction-diffusion equations
-
A. Doelman, R. A. Gardner, T. Kaper, Large Stable Pulse Solutions in Reaction-Diffusion Equations, Indiana U. Math. J., 50(1), (2001), pp. 443-507. (Pubitemid 33589973)
-
(2001)
Indiana University Mathematics Journal
, vol.50
, Issue.1
, pp. 443-507
-
-
Doelman, A.1
Gardner, R.A.2
Kaper, T.J.3
-
9
-
-
0347670293
-
n-Splitting or Edge-Splitting? A Manner of Splitting in Dissipative Systems
-
S. Ei, Y. Nishiura, K. Ueda, 2n Splitting or Edge Splitting?: A Manner of Splitting in Dissipative Systems, Japan. J. Ind. Appl. Math., 18, (2001), pp. 181-205. (Pubitemid 33679055)
-
(2001)
Japan Journal of Industrial and Applied Mathematics
, vol.18
, Issue.2
, pp. 181-205
-
-
Ei, S.-I.1
Nishiura, Y.2
Ueda, K.-I.3
-
10
-
-
0006030342
-
The motion of weakly interacting pulses in reaction-diffusion systems
-
S. Ei, The Motion of Weakly Interacting Pulses in Reaction-Diffusion Systems, J. Dyn. Diff. Eq., 14, no. 1, (2002), pp. 85-137.
-
(2002)
J. Dyn. Diff. Eq.
, vol.14
, Issue.1
, pp. 85-137
-
-
Ei, S.1
-
11
-
-
0015454185
-
A theory of biological pattern formation
-
A. Gierer, H. Meinhardt, A Theory of Biological Pattern Formation, Kybernetik, 12, (1972), pp. 30-39.
-
(1972)
Kybernetik
, vol.12
, pp. 30-39
-
-
Gierer, A.1
Meinhardt, H.2
-
12
-
-
0001067122
-
Order and localization in reaction-diffusion pattern
-
L. Harrison, D. Holloway, Order and Localization in Reaction-Diffusion Pattern, Physica A, 222, (1995), pp. 210-233.
-
(1995)
Physica A
, vol.222
, pp. 210-233
-
-
Harrison, L.1
Holloway, D.2
-
13
-
-
0036665085
-
The dynamics of multi-spike solutions to the one-dimensional gierer-meinhardt model
-
electronic
-
D. Iron, M. J.Ward, The Dynamics of Multi-Spike Solutions to the One-Dimensional Gierer-Meinhardt Model, SIAM J. Appl. Math., 62(6), (2002), pp. 1924-1951 (electronic).
-
(2002)
SIAM J. Appl. Math.
, vol.62
, Issue.6
, pp. 1924-1951
-
-
Iron, D.1
Ward, M.J.2
-
14
-
-
0035277877
-
The stability of spike solutions to the one-dimensional gierer-meinhardt model
-
D. Iron, M. J.Ward, J.Wei, The Stability of Spike Solutions to the One-Dimensional Gierer-Meinhardt Model, Physica D, 150(1-2), (2001), pp. 25-62.
-
(2001)
Physica D
, vol.150
, Issue.1-2
, pp. 25-62
-
-
Iron, D.1
Ward, M.J.2
Wei, J.3
-
15
-
-
0018003001
-
Activators and inhibitors in pattern formation
-
J. Keener, Activators and Inhibitors in Pattern Formation, Stud. Appl. Math., 59, (1978), pp. 1-23.
-
(1978)
Stud. Appl. Math.
, vol.59
, pp. 1-23
-
-
Keener, J.1
-
16
-
-
0002542873
-
Large amplitude stationary solutions to a chemotaxis system
-
C. S. Lin,W. M. Ni, I. Takagi, Large Amplitude Stationary Solutions to a Chemotaxis System, J. Diff. Eq., 72, (1988), pp. 1-27.
-
(1988)
J. Diff. Eq.
, vol.72
, pp. 1-27
-
-
Lin, C.S.1
Ni, W.M.2
Takagi, I.3
-
19
-
-
84867986083
-
-
NAG Fortran Library Mark 17, routine D03PCF,Numerical Algorithms Group Ltd., Oxford, United Kingdom (1995)
-
NAG Fortran Library Mark 17, routine D03PCF, Numerical Algorithms Group Ltd., Oxford, United Kingdom (1995).
-
-
-
-
20
-
-
0003002827
-
Diffusion cross-diffusion and their spike-layer steady-states
-
W. Ni, Diffusion, Cross-Diffusion, and Their Spike-Layer Steady-States, Not. AMS, 45(1), (1998), pp. 9-18.
-
(1998)
Not. AMS
, vol.45
, Issue.1
-
-
Ni, W.1
-
21
-
-
84867984486
-
-
to appear, Tohoku Math J.
-
W. Ni, I. Takagi, E. Yanagida, Stability Analysis of Point-Condensation Solutions to a Reaction-Diffusion System Proposed by Gierer and Meinhardt, to appear, Tohoku Math J., (2002).
-
(2002)
Stability Analysis of Point-Condensation Solutions to A Reaction-Diffusion System Proposed by Gierer and Meinhardt
-
-
Ni, W.1
Takagi, I.2
Yanagida, E.3
-
22
-
-
0001347301
-
Global structure of bifurcating solutions of some reaction-diffusion systems
-
Y. Nishiura, Global Structure of Bifurcating Solutions of Some Reaction-Diffusion Systems, SIAM J. Math. Anal., 13(4), (1982), pp. 555-593.
-
(1982)
SIAM J. Math. Anal.
, vol.13
, Issue.4
, pp. 555-593
-
-
Nishiura, Y.1
-
23
-
-
0002882425
-
Coexistence of infinitely many stable solutions to reaction-diffusion equations in the singular limit
-
editors: C. K. R. T. Jones, U. Kirchgraber), Springer-Verlag, New York
-
Y. Nishiura, Coexistence of Infinitely Many Stable Solutions to Reaction-Diffusion Equations in the Singular Limit, in Dynamics Reported: Expositions in Dynamical Systems, vol. 3 (editors: C. K. R. T. Jones, U. Kirchgraber), Springer-Verlag, New York (1995).
-
(1995)
Dynamics Reported: Expositions in Dynamical Systems
, vol.3
-
-
Nishiura, Y.1
-
24
-
-
0035311814
-
Spatio-temporal chaos for the Gray-Scott model
-
DOI 10.1016/S0167-2789(00)00214-1
-
Y. Nishiura, D. Ueyama, Spatio-Temporal Chaos for the Gray-Scott Model, Physica D, 150, (2001), pp. 137-162. (Pubitemid 32265308)
-
(2001)
Physica D: Nonlinear Phenomena
, vol.150
, Issue.3-4
, pp. 137-162
-
-
Nishiura, Y.1
Ueyama, D.2
-
25
-
-
1642548932
-
Far-from-equilibrium dynamics
-
AMS Publications, Providence, RI
-
Y. Nishiura, Far-from-Equilibrium Dynamics, Translations of Mathematical Monographs, vol. 209, AMS Publications, Providence, RI (2002).
-
(2002)
Translations of Mathematical Monographs
, vol.209
-
-
Nishiura, Y.1
-
26
-
-
0018784247
-
Simple chemical reaction systems with limit cycle behavior
-
J. Schnakenberg, Simple Chemical Reaction Systems with Limit Cycle Behavior, J. Theor. Biol., 81, (1979), pp. 389-400.
-
(1979)
J. Theor. Biol.
, vol.81
, pp. 389-400
-
-
Schnakenberg, J.1
-
27
-
-
84867984485
-
Numerical challenges for resolving spike dynamics for two reaction-diffusion systems
-
W. Sun, T. Tang, M. J. Ward, J. Wei, Numerical Challenges for Resolving Spike Dynamics for Two Reaction-Diffusion Systems, accepted, Stud. Appl. Math., (2002).
-
(2002)
Stud. Appl. Math.
-
-
Sun, W.1
Tang, T.2
Ward, M.J.3
Wei, J.4
-
28
-
-
0000864203
-
Point-condensation for a reaction-diffusion system
-
I. Takagi, Point-Condensation for a Reaction-Diffusion System, J. Diff. Eq., 61, (1986), pp. 208-249.
-
(1986)
J. Diff. Eq.
, vol.61
, pp. 208-249
-
-
Takagi, I.1
-
29
-
-
0002011401
-
The chemical basis of morphogenesis
-
A. Turing, The Chemical Basis of Morphogenesis, Phil. Trans. Roy. Soc. B, 327, (1952), pp. 37-72.
-
(1952)
Phil. Trans. Roy. Soc. B
, vol.327
, pp. 37-72
-
-
Turing, A.1
-
30
-
-
0036067340
-
Asymmetric spike patterns for the one-dimensional gierer-meinhardt model: Equilibria and stability
-
M. J. Ward, J. Wei, Asymmetric Spike Patterns for the One-Dimensional Gierer-Meinhardt Model: Equilibria and Stability, Eur. J. Appl. Math., 13(3), (2002), pp. 283-320.
-
(2002)
Eur. J. Appl. Math.
, vol.13
, Issue.3
, pp. 283-320
-
-
Ward, M.J.1
Wei, J.2
-
31
-
-
84867986086
-
Hopf bifurcation of spike solutions for the shadow gierer-meinhardt model
-
M. J. Ward, J. Wei, Hopf Bifurcation of Spike Solutions for the Shadow Gierer-Meinhardt Model, submitted, Eur. J. Appl. Math., (2002).
-
(2002)
Eur. J. Appl. Math.
-
-
Ward, M.J.1
Wei, J.2
-
32
-
-
0033414750
-
On single interior spike solutions for the gierer-meinhardt system: Uniqueness and stability estimates
-
J.Wei, On Single Interior Spike Solutions for the Gierer-Meinhardt System: Uniqueness and Stability Estimates, Eur. J. Appl. Math., 10(4), (1999), pp. 353-378.
-
(1999)
Eur. J. Appl. Math.
, vol.10
, Issue.4
, pp. 353-378
-
-
Wei, J.1
-
33
-
-
30244514666
-
The gierer-meinhardt system: Existence and stability of n-peaked Solutions
-
J. Wei, M. Winter, The Gierer-Meinhardt System: Existence and Stability of N-Peaked Solutions, submitted, Trans. Am. Math Soc., (2001).
-
(2001)
Trans. Am. Math Soc.
-
-
Wei, J.1
Winter, M.2
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