In this paper, we show that the Gray-Scott model is able to produce defect-mediated turbulence. This regime emerges from the limit cycle, close or far from the Hopf bifurcation, but always right before the Andronov homoclinic bifurcation of the homogeneous system. After this bifurcation, as the control parameter is further changed, the system starts visiting more and more frequently the stable node of the model. Consequently, the defect-mediated turbulence gradually turns into spatiotemporal intermittency.

1.
B. I.
Shraiman
,
A.
Pumir
,
W.
Van Saarloos
,
P. C.
Hohenberg
,
H.
Chaté
, and
M.
Holen
,
Phys. D
57
,
241
248
(
1992
).
2.
Q.
Ouyang
and
J. M.
Flesselles
,
Nature
379
,
143
(
1996
).
3.
I.
Berenstein
and
C.
Beta
,
J. Chem. Phys.
135
,
164901
(
2011
).
4.
C.
Beta
,
A. S.
Mikhailov
,
H. H.
Rotermund
, and
G.
Ertl
,
Europhys. Lett.
75
,
868
874
(
2006
).
5.
K.
Krischer
,
M.
Eiswirth
, and
G.
Ertl
,
J. Chem. Phys.
96
,
9161
(
1992
);
D.
Krefting
and
C.
Beta
,
Phys. Rev. E
81
,
036209
(
2010
).
6.
M.
Bär
,
M.
Hildebrand
,
M.
Eiswirth
,
M.
Falke
,
H.
Engel
, and
M.
Neufeld
,
Chaos
4
,
499
(
1994
).
7.
Q.
Zhuang
,
X.
Gao
,
Q.
Ouyang
, and
H.
Wang
,
Chaos
22
,
043133
(
2012
).
8.
P.
Coullet
,
L.
Gil
, and
J.
Lega
,
Phys. Rev. Lett.
62
,
1619
(
1989
).
9.
J.
Davidsen
and
R.
Kapral
,
Phys. Rev. Lett.
91
,
058303
(
2003
).
10.
P.
Gray
and
S. K.
Scott
,
Chem. Eng. Sci.
39
,
1087
1097
(
1984
).
11.
J. H.
Merkin
,
V.
Petrov
,
S. K.
Scott
, and
K.
Showalter
,
Phys. Rev. Lett.
76
,
546
(
1996
);
[PubMed]
R.
Wackerbauer
and
K.
Showalter
,
Phys. Rev. Lett.
91
,
174103
(
2003
).
[PubMed]
12.
M.
Argentina
and
P.
Coullet
,
Phys. A
257
,
45
60
(
1998
).
13.
Y.
Nashiura
and
D.
Ueyama
,
Phys. D
150
,
137
162
(
2001
).
14.
M.
Bertram
and
A. S.
Mikhailov
,
Phys. Rev. E
63
,
066102
(
2001
).
15.
I.
Berenstein
and
C.
Beta
,
Phys. Rev. E
86
,
056205
(
2012
).
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