The concentration profiles along the feeding direction of a one side fed gel reactor are analyzed for the iodate-arsenous acid reaction. Multiplicity of inhomogeneous stationary solutions is derived. It is also shown that such profiles may undergo oscillatory bifurcations under long range activation conditions. The bifurcation diagram is analyzed using a Galerkin approximation, the asymptotic validity of which is discussed.

1.
P.
Blanchedeau
,
J.
Boissonade
, and
P.
De Kepper
,
Physica D
147
,
283
(
2000
).
2.
P.
Borckmans
,
G.
Dewel
,
A.
De Wit
,
E.
Dulos
,
J.
Boissonade
,
F.
Gauffre
, and
P.
De Kepper
,
Int. J. Bifurcation Chaos Appl. Sci. Eng.
12
,
2307
(
2002
).
3.
J.
Boissonade
,
P.
De Kepper
,
F.
Gauffre
, and
I.
Szalai
,
Chaos
3
,
037110
(
2006
) (this issue).
4.
J.
Boissonade
,
E.
Dulos
,
F.
Gauffre
,
M. N.
Kuperman
, and
P.
De Kepper
,
Faraday Discuss.
120
,
253
(
2001
).
5.
M.
Fuentes
,
M. N.
Kuperman
,
J.
Boissonade
,
E.
Dulos
,
F.
Gauffre
, and
P.
Kepper
,
Phys. Rev. E
66
,
056205
(
2002
).
6.
I. R.
Epstein
and
J. A.
Pojman
,
An Introduction to Nonlinear Chemical Dynamics
(
Oxford University Press
,
Oxford
,
1998
).
7.
V.
Castets
,
E.
Dulos
,
J.
Boissonade
, and
P.
De Kepper
,
Phys. Rev. Lett.
64
,
2953
(
1990
).
8.
Q.
Ouyang
and
H.
Swinney
,
Nature (London)
352
,
610
(
1991
).
9.
B.
Rudovics
,
E.
Barillot
,
P. W.
Davies
,
E.
Dulos
,
J.
Boissonade
, and
P.
De Kepper
,
J. Phys. Chem. A
103
,
1790
(
1999
).
10.
K. J.
Lee
,
W. D.
McCormick
,
Q.
Ouyang
, and
H. L.
Swinney
,
Science
261
,
192
(
1993
).
11.
K.
Benyaich
, Ph.D. thesis,
Université Libre de Bruxelles
(
2005
).
12.
P. B.
Weisz
and
J. S.
Hicks
,
Chem. Eng. Sci.
17
,
265
(
1962
).
13.
R.
Aris
,
Chem. Eng. Sci.
24
,
149
(
1969
).
14.
D.
Luss
in
Spatial Inhomogeneities and Transient Behaviour in Chemical Kinetics
, edited by
P.
Gray
,
G.
Nicolis
,
F.
Baras
,
P.
Borckmans
,
S.
Scott
(
Manchester University Press
,
Manchester
,
1989
), p.
103
, and references therein.
15.
J.
Shi
, Ph.D. thesis,
Brigham Young University
(
2003
).
16.
P.
Gray
and
S.
Scott
,
Chemical Oscillations and Instabilities
(
Oxford University Press
,
Oxford
,
1990
).
17.
R.
Lefever
,
M.
Herschkowitz-Kaufman
, and
J. W.
Turner
,
Phys. Lett.
60A
,
389
(
1977
).
18.
A.
Saul
and
K.
Showalter
in
Oscillating and Traveling Waves in Chemical Systems
, edited by
R. J.
Field
and
M.
Burger
(
Wiley
,
New York
,
1985
), p.
419
.
19.
D.
Horvath
,
V.
Petrov
,
S. K.
Scott
, and
K.
Showalter
,
J. Chem. Phys.
98
,
6332
(
1993
).
20.
D.
Horvath
and
K.
Showalter
,
J. Chem. Phys.
102
,
2471
(
1995
).
21.
N.
Ganapathisubramanian
and
K.
Showalter
,
J. Chem. Phys.
84
,
5427
(
1983
).
22.
G.
Dewel
,
P.
Borckmans
, and
D.
Walgraef
,
J. Phys. Chem.
88
,
5442
(
1984
).
23.
M.
Golubitsky
and
D. G.
Shaeffer
,
Singularites and Groups in Bifurcations Theory
(
Springer Verlag
,
Berlin
,
1985
).
24.
J.
Boissonade
and
P.
De Kepper
,
J. Phys. Chem.
84
,
501
(
1980
).
25.
J. P.
Keener
,
Chem. Phys.
18
,
126
(
1981
).
26.
J. P.
Keener
,
SIAM J. Appl. Math.
41
,
127
(
1981
).
27.
M.
Baer
and
T.
Erneux
,
SIAM J. Appl. Math.
46
,
721
(
1986
);
M.
Baer
and
T.
Erneux
,
SIAM J. Appl. Math.
52
,
1651
(
1992
).
28.
P. A.
Braza
and
T.
Erneux
,
Phys. Rev. A
40
,
2539
(
1989
).
29.
A.
De Wit
,
P.
De Kepper
,
K.
Benyaich
,
G.
Dewel
, and
P.
Borckmans
,
Chem. Eng. Sci.
58
,
4823
(
2003
).
30.
S.
Villain
,
S.
Métens
, and
P.
Borckmans
,
J. Mech. Behav. Mater.
(to be published).
31.
J.
Boissonade
,
Phys. Rev. Lett.
90
,
188302
(
2003
);
J.
Boissonade
,
Chaos
15
,
023703
(
2005
).
You do not currently have access to this content.