Coexistence of two bifurcation regimes in a closed ferroin-catalyzed Belousov-Zhabotinsky reaction

Article abstract of DOI:10.1021/jp0456279

The ferroin-catalyzed Belousov-Zhabotinsky (BZ) reaction was studied in a batch reactor under anaerobic conditions and was found to evolve through two separated regimes of complex oscillations. Significantly, the two bifurcation regimes exhibited qualitatively different dependence on compositions of the reaction mixture, i.e., initial concentrations of bromate, sulfuric acid, malonic acid, and ferroin. The reaction temperature also showed opposite effects on the two bifurcation regimes, in which complexities of the first bifurcation regime were enhanced while oscillations in the second bifurcation regime became simpler as a result of decreasing temperature. Numerical simulations with a 12-variable model developed specifically for the ferroin-BZ system were able to reproduce transient complex oscillations observed in experiments. These calculations further illustrated that reactions such as ferroin and HOBr, ferroin and HBrO₂, and ferriin and Br^- were not essential in describing complex dynamics of the ferroin-BZ reaction.

Full text of DOI:10.1021/jp0456279

1374
J. Phys. Chem. A 2005, 109, 1374-1381
Coexistence of Two Bifurcation Regimes in a Closed Ferroin-Catalyzed
Belousov-Zhabotinsky Reaction
,†
†
†
,‡
‡
Jichang Wang,* Jinpei Zhao, Yu Chen, Qingyu Gao,* and Yumei Wang
Department of Chemistry and Biochemistry, The UniVersity of Windsor, Windsor, ON N9B 3P4, Canada, and
College of Chemical Engineering, China UniVersity of Mining and Technology, Xuzhou, Jiangsu ProVince,
2
21008, People’s Republic of China
ReceiVed: September 26, 2004; In Final Form: NoVember 27, 2004
The ferroin-catalyzed Belousov-Zhabotinsky (BZ) reaction was studied in a batch reactor under anaerobic
conditions and was found to evolve through two separated regimes of complex oscillations. Significantly, the
two bifurcation regimes exhibited qualitatively different dependence on compositions of the reaction mixture,
i.e., initial concentrations of bromate, sulfuric acid, malonic acid, and ferroin. The reaction temperature also
showed opposite effects on the two bifurcation regimes, in which complexities of the first bifurcation regime
were enhanced while oscillations in the second bifurcation regime became simpler as a result of decreasing
temperature. Numerical simulations with a 12-variable model developed specifically for the ferroin-BZ system
were able to reproduce transient complex oscillations observed in experiments. These calculations further
-
illustrated that reactions such as ferroin and HOBr, ferroin and HBrO
in describing complex dynamics of the ferroin-BZ reaction.
2
, and ferriin and Br were not essential
1
. Introduction
are extremely susceptible to variations of reaction parameters
and thus have particular advantages in characterizing the
underlying reaction mechanism. Transient complex oscillations
including consecutive period-doubling bifurcations, torus oscil-
The study of nonlinear chemical dynamics has flourished in
the past four decades,1-6 which led to the observation of a
variety of nonlinear spatial and temporal behaviors in various
lations, and transient chaos have been reported earlier in the
chemical and biochemical reactions.7
-16
The striking color
37-39
cerium-catalyzed BZ reaction.
In the closed ferroin-
changes between oxidized and reduced states in the Belousov-
catalyzed BZ reaction, only mixed-mode oscillations were
Zhabotinsky (BZ) reaction (due to the presence of metal catalysts
40
reported by Strizhak and co-workers. As shown in the
such as Ru(bpy)33 /Ru(bpy)3 and Fe(phen)3 /Fe(phen)3
+
2+
3+
2+
)
following, this study revealed that the ferroin-catalyzed BZ
system was capable of exhibiting two isolated bifurcation
regimes even under closed reaction conditions, which resembled
the two bifurcation regions observed, respectively, at high and
provided a convenient way to investigate pattern formation in
a spatially extended medium.1
7-28
As a result, despite the
discovery of numerous new chemical oscillators in the past two
decades, the BZ reaction remains a prototype model in studies
of nonlinear dynamics.1
low flow rates in a continuous flow stirred tank reactor
7-42
29,30
(CSTR).
The mixed-mode oscillations reported earlier by
Mechanisms of the BZ reaction have been understood largely
based on the Field-K o¨ r o¨ s-Noyes (FKN) theory, which was
developed to account for the behavior observed primarily in
the cerium-catalyzed BZ reaction.3 In recent studies, however,
Gaspar and co-workers showed that, when ferroin was used as
the metal catalyst, the behavior of the BZ reaction could not be
accounted by simply modifying rate constants of a few
elementary steps of the FKN theory.35 They suggested that
possible reactions between ferriin and bromide and between
ferroin and bromine, HOBr, etc. should also be considered in
the model developed specifically for the ferroin-catalyzed BZ
system.3
To shed light on the understanding of the ferroin-catalyzed
BZ reaction mechanism, in this study we systematically
characterized the dynamic behavior of the ferroin-BZ reaction
in a batch reactor under anaerobic conditions. Our attention was
particularly focused on searching for new transient complex
oscillations in the above system, because complex oscillations
Strizhak and co-workers appeared to correspond to the complex
behavior that occurred within the first bifurcation regime in this
study. Notably, period-doubled oscillations in the second
bifurcation regime lasted for as long as 5 h and thus could be
conveniently employed to investigate pattern formation under
4
43,44
period-doubled oscillation dynamics.
2. Experimental Procedures
All reactions were carried out in a thermostated glass vessel,
where the temperature was controlled at 20.0 ( 0.1 °C by a
circulating water bath (NatLab, RTE 10). Reactions were
followed by a platinum electrode coupled with a Hg|Hg2SO4|K2-
SO4 reference electrode. The potential was recorded with a
personal computer connected through an electrochemistry
station, VoltaLab 10 (Radiometer). A bromide ion selective
electrode (Orion, 9435BN) coupled with the calomel reference
electrode was also employed to follow the evolution of the
reaction, and qualitatively the same behavior was observed.
Stock solutions of 1.0 M NaBrO3 (Aldrich, 99%), 0.8 M malonic
acid (Aldrich, 98%), and 3 M sulfuric acid (Aldrich, 98%) were
dissolved in double distilled water. Ferroin, 0.025 M, was
prepared with FeSO4‚7H2O (Aldrich) and 1,10-phenanthroline
5,36
*
Corresponding authors. Fax, (519) 973-7098; e-mail, jwang@uwindsor.ca
(
J.W.). Fax, 86-516-3995758; e-mail, gaoqy@cumt.edu.cn (Q.G.).
†
‡
The University of Windsor.
China University of Mining and Technology.
1
0.1021/jp0456279 CCC: $30.25 © 2005 American Chemical Society
Published on Web 01/28/2005

Ferroin-Catalyzed Belousov-Zhabotinsky Reaction
J. Phys. Chem. A, Vol. 109, No. 7, 2005 1375
before spontaneous oscillations emerged. Interestingly, within
the first 500 s every large peak was followed by a small peak,
resembling the mode of mixed mode oscillations. As the
amplitude of these small peaks increased in time, the BZ reaction
smoothly evolved into simple period-1 oscillations. Similar
phenomena have been reported earlier by Strizhak and co-
workers under quite different reaction conditions, where con-
centrations of malonic acid and bromate were almost twice as
40
high as those used in this study. Significantly, period-doubled
oscillations appeared again at about t ) 3200 s, followed by
other modes of complex oscillations. In contrast to the short
lifetime of the first group of period-doubled oscillations, the
second bifurcation sequence lasted for more than 4 h. Between
the two regimes of complex oscillations, there was a period of
simple period-1 oscillations (ca. 30 min). Note that, unlike in a
CSTR, where a bifurcation parameter such as flow rate can be
well-defined, in a batch reactor everything is transient except
the final thermodynamic equilibrium state. Nevertheless, con-
centrations of initial reactants in a batch reaction could be
viewed as a bifurcation control parameter, which decreases
continuously in time. If the decrease in the concentration of
reactants is slow enough, which corresponds to slowly varying
the bifurcation parameter such as flow rate in a CSTR, evolution
of a batch reaction would be able to reflect the dynamic behavior
occurring at the corresponding bifurcation conditions. The
phenomenon shown above thus illustrates that the closed ferroin-
BZ reaction evolves through two bifurcation regimes, where
the first bifurcation regime occurs as soon as spontaneous
oscillations begin.
BrMA has been suggested to play an essential role in the
development of complex oscillations in the cerium-BZ reac-
4
2,45
tion,
in which transient complex oscillations would not occur
37-39
until the concentration of BrMA has reached a certain level.
However, in the system studied here the first bifurcation regime
appeared right after the start of spontaneous oscillations, in
which there was an unlikely large amount of BrMA in the
solution. Therefore, BrMA may not play a critical role in the
occurrence of the first bifurcation sequence in this study, or
alternatively, the ferroin-BZ system is so sensitive to the
Figure 1. Time series showing evolution of ferroin-catalyzed Be-
lousov-Zhabotinsky reaction in a closed system. Initial compositions
-
production of Br that it does not require the presence of a
large amount of BrMA. To shed light on the above issue, a
series of experiments in the initial presence of BrMA were
conducted in which BrMA was prepared by adding different
amounts of bromide into the reaction mixture. These studies
illustrated that when [BrMA] ) 0.001 M the total numbers of
mixed-mode oscillations within the first bifurcation regime were
doubled and even the pattern of one large and two small peaks
of the reaction mixture are [H
2
SO
4
] ) 0.38 M, [MA] ) 0.30 M, [ferroin]
-
4
-
)
5.0 × 10 M, and [BrO
3
] ) 0.10 M.
(Aldrich) according to a 1:3 stoichiometric relationship. All
chemicals were used in their commercial grade without further
purification.
The volume of the reaction mixture was kept constant at 30.0
mL throughout this study. There was about 1 cm gap between
the solution and the bottom of the lid. To avoid the influence
of oxygen, nitrogen gas was continuously flowed into the gap
at a speed of about 0.05 L/min. To examine any kinetic influence
imposed by the flow of nitrogen gas, argon was occasionally
used at a much lower flow rate (<0.01 L/min). No difference
in the reaction behavior was recorded there. To reduce the
amount of oxygen presented initially in these stock solutions,
sodium bromate, malonic acid, and sulfuric acid were mixed
first in the reactor and the mixture was stirred for 15 min under
nitrogen environment.
2
per cycle (1 ) could be observed there. In contrast, no significant
influence on oscillations of the second bifurcation sequence was
seen. Further increase of BrMA concentration (>0.0025 M)
prolonged the first bifurcation regime dramatically, but elimi-
nated the second bifurcation regime. These results illustrate that
BrMA still plays an important role in the complex oscillations
in the ferroin-catalyzed BZ reaction; however, the two bifurca-
tion regimes are likely governed by different mechanisms.
To gain further insight into the dynamics of the two
bifurcation regimes, initial compositions of the reaction solution
were adjusted systematically in the following experiments. In
Figure 2, the concentration of ferroin was decreased gradually,
while all other reaction conditions were kept the same as those
in Figure 1. Note that Figure 2a shows the first 1100 s of the
corresponding time series collected in Figure 2b. Mixed-mode
oscillations including patterns of one large and two small peaks
3
. Experimental Results
Figure 1 presents a time series obtained under the following
initial compositions: [H2SO4] ) 0.38 M, [MA] ) 0.30 M,
-
4
-
[
ferroin] ) 5.0 × 10 M, and [BrO3 ] ) 0.10 M. As reported
1
2
in earlier investigations, there was a short induction period
per cycle (1 ) can be seen in the time series Figure 2a(I), where

1376 J. Phys. Chem. A, Vol. 109, No. 7, 2005
Wang et al.
-
4
-4
-4
Figure 2. Time series of BZ reaction under different initial concentrations of ferroin: (I) 10.0 × 10 M, (II) 4.0 × 10 M, and (III) 2.0 × 10
M. Other reaction conditions are the same as those in Figure 1. Part a plots the first 1100 s of the corresponding time series in (b).
-
4
[
ferroin] ) 10.0 × 10 M. These mixed-mode oscillations
M. Other reaction conditions are the same as those in Figure 1.
Initially, both the complexity and lifetime of the first bifurcation
regime were increased as bromate concentration was decreased
from 0.11 M in series I to 0.09 M in series II. Interestingly, in
the time series Figure 4a(III) a new small amplitude peak
developed at the bottom of two consecutive large peaks while
the original small peak of the mixed-mode oscillations could
still, though barely, be seen. Careful examination of the time
series Figure 4b(III) illustrates that the insertion of the new small
peak is due to the two bifurcation regimes merging under this
set of reaction conditions. If the concentration of bromate was
decreased still (see time series IV), these new peaks occurring
in the time series Figure 4a(III) disappeared again. Such a result
was because the second bifurcation regime diminished under
those conditions (see the complete time series Figure 4b(IV)).
Notably, when bromate concentration was adjusted as the only
variable, the second bifurcation regime disappeared first. Figure
become simpler and last for a shorter period of time in the time
series Figure 2a(II), in which ferroin concentration was de-
-4
creased to 5.0 × 10 M. The first bifurcation regime diminished
completely in the time series Figure 2a(III) when ferroin
-
4
concentration was decreased to 2.0 × 10 M. As shown in
Figure 2b, the second group of complex oscillations in both
series I and II did not begin until the first bifurcation regime
disappeared more than 25 min. In contrast to the first bifurcation
sequence, complexities of the second bifurcation regime (see
Figure 2b) were actually enhanced as the result of decreasing
the concentration of ferroin. The second bifurcation regime also
lasted longer at lower ferroin concentration, which was, again,
opposite what happened to the first bifurcation regime.
Figure 3 shows effects of MA concentration on the two
bifurcation regimes, in which the initial concentration of MA
is (I) 0.40 M, (II) 0.30 M, and (III) 0.20 M. Other reaction
conditions are the same as those in Figure 1, i.e., [H2SO4] )
4
also indicates that there was an optimum range of bromate
-
4
-
0
.38 M, [ferroin] ) 5.0 × 10 M, and [BrO3 ] ) 0.10 M.
concentration for the development of both the first and the
second bifurcation regimes in the ferroin-BZ reaction. Such a
phenomenon is somehow different from what was reported in
the cerium-catalyzed BZ reaction, in which increasing bromate
concentration seemed to always enhance the complexity of
Again, Figure 3a presents the first 1100 s of the corresponding
time series collected in Figure 3b. Results in Figure 3a illustrate
that the first bifurcation regime lasted for a shorter period of
time as the concentration of MA was decreased. Meanwhile,
the complexity of these mixed-mode oscillations also appears
to be reduced as the pattern of one large and two small peaks
3
7
transient oscillations.
2
Figure 5 illustrates the influence of the concentration of
sulfuric acid on the ferroin-BZ reaction, in which Figure 5a
presents the first 1800 s of the corresponding time series
collected in Figure 5b. Again, all reaction conditions were kept
the same as those in Figure 1, except that H2SO4 concentration
was adjusted to 0.30 M in (I) and 0.2 M in (II). As shown in
Figure 5a(I), the first bifurcation regime lasted for a longer
period of time than that in Figure 1 in which [H2SO4] ) 0.38
M. Complex oscillations in the second bifurcation regime also
became more irregular, in which period-2 oscillations mingled
with other modes of oscillations such as oscillations of one small
and two large peaks per cycle. Careful examination of the time
per cycle (1 ) can be seen at [MA] ) 0.4 M but not at [MA] )
.3 or 0.2 M. When the concentration of MA became smaller
0
than 0.1 M, the first bifurcation regime disappeared. Under all
three conditions characterized here, on the other hand, there
was no dramatic change in the behavior of the second bifurcation
regime, although complex oscillations in the second bifurcation
regime appeared to become slightly irregular at higher MA
concentration. The second bifurcation regime in all three cases
continued for about the same amount of time (≈300 min).
Influences of bromate concentration on the above sequential
bifurcation regimes are summarized in Figure 4, in which
BrO3 ] is (I) 0.11 M, (II) 0.09 M, (III) 0.07 M, and (IV) 0.06
-
[

Ferroin-Catalyzed Belousov-Zhabotinsky Reaction
J. Phys. Chem. A, Vol. 109, No. 7, 2005 1377
Figure 3. Time series of BZ reaction under different initial concentrations of MA: (I) 0.40 M, (II) 0.30 M, and (III) 0.20 M. Other reaction
conditions are the same as those in Figure 1. Part a plots the first 1100 s of the corresponding time series in (b).
Figure 4. Time series of BZ reaction under different initial concentrations of bromate: (I) 0.11 M, (II) 0.09 M, (III) 0.07 M, and (IV) 0.06 M.
Other reaction conditions are the same as those in Figure 1. Part a plots the first 1200 s of the corresponding time series in (b).
series Figure 5b(I) indicates that the two bifurcation regimes
had already emerged here, in which large amplitude oscillations
underwent a bifurcation while the original mixed-mode oscil-
lations were still there (at t ≈ 1000 s). As sulfuric acid
concentration was decreased further to 0.2 M, only one
bifurcation regime was achieved in the time series Figure

1378 J. Phys. Chem. A, Vol. 109, No. 7, 2005
Wang et al.
Figure 5. Time series of BZ reaction under different initial concentrations of sulfuric acid: (I) 0.30 M and (II) 0.20 M. Other reaction conditions
are the same as those in Figure 1. Part a plots the first 1800 s of the corresponding time series in (b).
Figure 6. Time series of BZ reaction achieved under different reaction temperatures: (I) 25.0 °C and (II) 15.0 °C. Other reaction conditions are
the same as those in Figure 1. (a) and (b) are the results collected within different time intervals.
5
b(II), which looks like the overlap of the two bifurcation
regimes.
In Figure 6 reaction temperature was characterized as the only
bifurcation regime appear to be more complicated at higher
reaction temperature. The opposite response to temperature
change further indicates that complex oscillations in the two
bifurcation regimes are governed by different reaction mecha-
nisms.
variable while all other reaction conditions were kept the same
as those in Figure 1. When the temperature was increased to
25.0 °C, the total numbers of complex oscillations within the
first bifurcation regime were reduced to two. If the temperature
was decreased from the reference experiment shown in Figure
4
. Computational Results
1, the first bifurcation sequence became richer and lasted longer
As discussed earlier, Keki and co-workers suggested that
as shown in the time series Figure 6a(II), where not only the
reactions between ferriin and bromide and between ferroin and
HBrO2, HOBr, Br2, etc. shall also be considered when simulating
the ferroin-catalyzed BZ system. Working from the same
1
pattern of one large and one small peak per cycle (1 ) but also
2
35
oscillations of one large and two small peaks per cycle (1 ) can
be seen. In contrast, complex oscillations in the second
viewpoint, Strizhak and co-workers proposed a model by

Ferroin-Catalyzed Belousov-Zhabotinsky Reaction
J. Phys. Chem. A, Vol. 109, No. 7, 2005 1379
TABLE 1a
concentration of bromate was too low, such as 0.06 M in the
time series Figure 7d, no complex oscillations occurred. On the
other hand, as the bromate concentration was increased, complex
oscillations became more complicated. Notably, in both parts a
and b of Figure 7, the small peak of the period-doubled
oscillations become invisible even under logarithmic scale at t
≈ 2000 s, implying that period-doubled oscillations tend to cease
here. Beyond that point, the small peak revived and became
more and more prominent in time. From a dynamic point of
view, such a scenario implicates that a reverse period-doubling
bifurcation takes place at t ≈ 1800 s to lead the system back to
simple oscillations, which is then followed by another forward
period-doubling bifurcation leading the system to complex
oscillations. In Figure 7c, the first group of period-doubled
oscillations, which appeared before t ) 1800 s, disappeared
spontaneously, while period-doubled oscillations which re-
sembled the second part of period-doubled oscillations shown
in Figure 7a,b were still there. This suggests that period-doubled
oscillations appearing before t ≈ 1800 s may correspond to the
first bifurcation regime observed in experiments, whereas
complex oscillations appearing after t ≈ 1800 s correspond to
the second bifurcation regime. Unfortunately, we failed to obtain
a few simple oscillations around t ) 1800 s, even though rate
constants as well as initial values of reactants had been tuned
delicately. In addition, as opposed to experimental observation,
the first group of period-doubled oscillations seen in the above
modeling does not appear as soon as spontaneous oscillations
begin. Further improvement of the model will be conducted in
our future work.
no.
reaction
rate const
-
-
+
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
Br + BrO
3
+ 2H f HOBr + HBrO
2
1.28
3.3
-
-
+
HOBr + HBrO
HBrO
2HOBr f HBrO
2
f Br + BrO
3
+ 2H
-
+
6
2
+ Br + H f 2HOBr
1.6 × 10
-
+
-5
2
+ Br + H
2 × 10
-
+
9
HOBr + Br + H f Br
2
+ H
2
O
1.84 × 10
-
+
Br
2
+ H
2
O f HOBr + Br + H
2
-
+
2HBrO
2
f BrO
3
+ HOBr + H
3000
-
+
-9
BrO
BrO
3
+ HOBr + H f 2HBrO
2
6.0 × 10
-
+
3
+ HBrO
+ H O f BrO
MA + Br f BrMA + Br + H
2
+ H f 2BrO
2
2
+ H O
40
-
+
7
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2BrO
2
2
3
+ HBrO
2
+ H
4.2 × 10
28.65
8.2
-
+
2
MA + HOBr f BrMA + H
2
O
BrMA + HOBr f product
0.1
8
2BrMA + H
2
O f BrMA + BrTTA
+ H O f HBrO + BrTTA
O f MA + BrTTA
f product
1 × 10
1
9
9
1
BrMA + BrO
2
2
2
5 × 10
1 × 10
5 × 10
32
BrMA + MA + H
2
MA + BrO
MA + BrO
2
-
+
3
+ H f BrO + product
2
-
BrTTA f Br + product
1
-
+
BrMA + BrO
3
+ H f BrO
2
+ BrTTA
+ H f Fe + HBrO
32
2
+
+
3+
7
Fe + BrO
2
2
7 × 10
0.256
1.6
2
+
-
+
3+
2Fe + BrO
2Fe + HBrO
3
+ 3H f 2Fe + HBrO
2
+ H
2
O
O
2
+
+
3+
3+
2
+ 2H f 2Fe + HOBr + H
2
2
+
+
-
-3
2Fe + HOBr + H f 2Fe + Br + H
2
O
5 × 10
2
+
+
3+
-
+
2Fe + Br + H f 2Fe + 2Br
- 2+
2
100
3
+
2Fe + 2Br f 2Fe + Br
2
+ H
b
3
+
2+
+
-2
Fe + MA f Fe + MA + H
1 × 10
3
+
2+
+
Fe + BrMA f Fe + BrMA + H
20
2
+
+
3+
7
Fe + BrMA + H f Fe + BrMA
5 × 10
a
+
[
H ] ) 0.8 M and [H
2
O
2
] ) 55.56 M are included in the rate
constants. Discussion regarding the election of these rate constants can
b
As discussed earlier, an essential difference between the FKN
mechanism and the model proposed by Strizhak and co-workers
is that Strizhak and co-workers considered reactions between
be found in ref 35. See ref 35.
incorporating those reactions suggested by Keki et al. to describe
complex oscillations in the ferroin-catalyzed BZ reaction
observed in a CSTR.36 Their model, listed in Table 1, consists
of 12 reagent species (variables) and 29 steps. Since the model
successfully reproduced the bifurcation sequence observed in
the CSTR, it was employed here as a prototype model to
simulate the ferroin-BZ reaction in a batch reactor. When the
model was directly applied to simulate the closed ferroin-
catalyzed BZ reaction, no complex oscillations could be seen
under the same conditions as employed in our experiments.
Indeed, no complex phenomena could be achieved in the
modeling even when initial concentrations of all reactants were
adjusted over a broad range.
To obtain transient complex oscillations, three rate constants,
namely, k15, k21, and k29, have been adjusted here. k15 was
increased to be 60 times higher while k21 and k29 became,
respectively, 7 and 40 times smaller than those values used by
Strizhak and co-workers.36 Discussions regarding the selection
of other rate constants can be found in the original work
published by Strizhak and co-workers. Our numerical simula-
tions illustrated that the complex dynamic behavior of the
ferroin-catalyzed BZ reaction was particularly sensitive to
variations of the following rate constants: k1, k15, k19, k21, k22,
and k29. For example, both increasing and decreasing the value
of k1 from that used in this study reduced the complexity of
BZ oscillations. Qualitatively the same kinds of influences were
observed when rate constants k15, k19, k21, k22, and k29 were
characterized individually.
An example of transient complex oscillations calculated from
the model is presented in Figure 7, in which the initial
concentration of bromate is (a) 0.11 M, (b) 0.09 M, (c) 0.07 M,
and (d) 0.06 M. Initial values of other reactants in the above
calculations matched those used in experiments. Similar to the
experimental observation (see Figure 4), when the initial
3
4,36
ferroin/ferriin and HOBr, Br , HBrO , etc.
2
2
To examine the
importance of those new steps in the development of complex
oscillations, we have respectively adjusted rate constants k ,
22
k , k , k , and k . Our calculations illustrated that variation
2
3
24 25
26
of k22 had significant effects on complex oscillations. Indeed,
complex oscillations could be obtained only when k22 was within
a proper range. However, when k , k , and k were changed
2
3
24
26
to 0, which corresponded to excluding those reactions from the
proposed mechanism, there was no change at all in the complex
oscillation pattern. When k25 was adjusted to 0, complex
oscillations became slightly simpler. For example, oscillations
shown in Figure 7a would become those shown in Figure 7b as
k25 was changed to 0.
5
. Conclusions
In this study, the ferroin-catalyzed BZ reaction was investi-
gated in a closed system and was found to evolve through two
bifurcation regimes. To the best of our knowledge, it is the first
example that a closed chemical system can exhibit such
complicated reaction dynamics. The two bifurcation regimes
exhibited qualitatively different dependence on initial composi-
tions of the reaction mixture and reaction temperature, suggest-
ing that complex oscillations in the two bifurcation regimes are
likely governed by different reaction processes. Such a conclu-
sion is further supported by the opposite responses of the two
bifurcation regimes to the addition of BrMA: increasing the
initial concentration of BrMA to above 0.0025 M dramatically
prolonged the first bifurcation regime; yet adverse effects on
the second bifurcation regime took place and the second
bifurcation regime diminished if [BrMA] > 0.005 M. Under
suitable reaction conditions, however, the two bifurcation
regimes can merge to produce new modes of oscillations such
as those shown in Figure 5b(II).
36

1380 J. Phys. Chem. A, Vol. 109, No. 7, 2005
Wang et al.
Figure 7. Time series of BZ oscillations calculated at different initial concentrations of BrO
3
-: (a) 0.11 M, (b) 0.09 M, (c) 0.07 M, and (d) 0.06
M. Rate constants used in this study are listed in Table 1. Initial concentrations of other reactants are the same as used in experiments. Initial values
of the intermediate species are all set to 0.
Numerical simulations with a model developed initially by
Strizhak and co-workers have successfully reproduced transient
complex oscillations observed in experiments. The bifurcation
sequence in the modeling also appears to consist of two regimes,
in which the first part of period-doubled oscillations disappears
simultaneously as a result of varying reaction parameters, i.e.,
decreasing BrO3- concentration. Unfortunately, no simple
oscillations (i.e., one peak per period) were obtained between
the two bifurcation regimes, despite adjustment of rate constants
as well as initial values of all reactants over a broad range. It is
interesting to point out that we found that the above model was
also capable of supporting sequential oscillations under certain
reaction conditions, although no such behavior has ever been
observed in our experiments. Whether it represents another
theory, complementing the radical mechanism suggested by
F o¨ rsterling et al., to explain the sequential oscillations observed
4
6
in the cerium-catalyzed BZ reaction will be explored in our
future work.

Ferroin-Catalyzed Belousov-Zhabotinsky Reaction
J. Phys. Chem. A, Vol. 109, No. 7, 2005 1381
Numerical simulations conducted in this study also illustrated
that eliminating the following three reaction steps from the
model listed in Table 1 had no influence on transient complex
oscillations:
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Acknowledgment. This work is supported by the National
Science and Engineering Research Council of Canada (NSERC)
and Canadian Foundation for Innovation (CFI). Q.G. thanks
NSFC (20103010) and EYTP of China for financial support.
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1
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