regularity of intermittent bursts in briggsrauscher oscillating systems with phenol

Regularity of Intermittent Bursts in Briggs�Rauscher Oscillating Systems withPhenol1)

by Zeljko D. Cupic*a), Ljiljana Z. Kolar-Anica)b), Slobodan R. Anica)b), Stevan R. Macesicb), Jelena P.Maksimovicb), Marko S. Pavlovicb), Maja C. Milenkovicb), Itana Nusa M. Bubanjab), Emanuela

Grecoc), Stanley D. Furrowd), and Rinaldo Cervellatic)

a) Institute of Chemistry, Technology and Metallurgy, University of Belgrade, Center of Catalysis andChemical Engineering, Njegoseva 12, RS-11000 Belgrade

(phone: þ 381-11-2630213; fax þ 381-11-2637977; e-mail: [email protected])b) Faculty of Physical Chemistry, University of Belgrade, Studentski trg 12 – 16, RS-11000 Belgradec) Dipartimento di Chimica �G. Ciamician�, Universita di Bologna, Via Selmi 2, IT-40126 Bologna

d) Emeritus, Berks College, Pennsylvania State University, Reading, PA 19610, USA

The intermittency or intermittent bursting as the type of dynamic state when two qualitativelydifferent behaviors replace one another randomly during the course of the reaction, although all thecontrol parameters remain constant, is found in the Briggs�Rauscher oscillating system moderated by avery small amount of phenol. Within a range of phenol concentrations, the oscillation amplitude isdiminished considerably, and after oscillations cease, they repeat intermittently, giving several bursts ofoscillations. For the concentrations used here, the range of phenol concentrations where intermittentbursting oscillations occur in a closed reactor is ca. 1.8� 10�5 to 3.6� 10�5

m. Bursting also occurs in anopen reactor and can be sustained indefinitely at 5.53� 10�5

m concentration. The intermittent burstingbehavior is robust, and can be achieved at a variety of conditions.

Introduction. – The Briggs�Rauscher (BR) oscillating system [1], typicallycontaining H2SO4 or HClO4, KIO3 or NaIO3, MnII or CeIII, organic substrate (usuallymalonic acid (MA)), H2O2, and starch, undergoes dramatic color changes as itoscillates several times per minute between clear, pale-yellow, and blue. The reaction isa favorite of demonstrators and chemical �magic� shows [2 – 5]. A robust model for theoscillator is still elusive.

The BR oscillatory reaction is examined under both batch (Fig. 1,a) andcontinuously stirred tank reactor (CSTR; Fig. 1,b) conditions.

Note that [I�] increases as potential decreases. In the batch reactor, under theconditions in Fig. 1, when oscillations ceased at ca. 43 min, the system was in a low-iodide, low-iodine state (called State I by Vanag) [6]. At ca. 45 min, there was atransition to a high iodide, high iodine state (State II). Solid iodine may precipitate inState II. Prolonged or permanent State I endings are favored by initial concentrationswith [MA]/[IO�

3 ] ratios > 2 : 1 [6] [7]. Immediate or rapid transitions to State II werefound for [MA]/[IO�

3 ] ratios (1 – 10) :1 [8]. Other initial concentrations have lessereffects.

Helvetica Chimica Acta – Vol. 97 (2014) 321

� 2014 Verlag Helvetica Chimica Acta AG, Z�rich

1) The very long and unusual history of this article demanded a large number of authors. Besidesprofessors, numerous students worked on experimental investigations.

It is known that the reaction is sensitive to many additives, many of which stop theoscillations for a time period which is linearly dependent on the additive concentration.As such, the reaction has been used as a quantitative measure of antioxidant activity[9]. A common property of many natural antioxidants is that they have multiplephenolic groups.

The compound phenol as an additive in a batch BR system gives rise to additionalphenomena: intermittent sequential oscillations (bursting), as discussed in the Resultssection, first noticed by one of us [10]. The oscillations are followed by a quiescentperiod or a period with a very low-amplitude oscillations, then further oscillations,repeated several times. Here, we will use the term intermittency or intermittentbursting for this type of dynamical state when two qualitatively different behaviorsreplace one another randomly during the course of the reaction, although all thecontrol parameters remain constant [11]. It is completely deterministic phenomenonresulting in nondeterministic (chaotic) dynamics.

Exploration of the batch system at different levels of phenol, and extension of thesame system to a continuously stirred tank reactor (CSTR) are the subjects of thiswork.

Experimental. – Batch Experiments. Several regions of MnII and MA concentrations, and some otherBR systems for which intermittences would occur have been examined previously in Bologna and at

Helvetica Chimica Acta – Vol. 97 (2014)322

Fig. 1. Time series, potential vs. time, for BR mixture with [HClO4]0¼ 0.10m. [KIO3]0¼ 0.020m, [MA]0¼0.016m, [MnSO4]0¼ 0.0020m, [H2O2]0¼ 1.2m, flow rate, 0.191 ml min�1. a) Batch reactor. b) CSTR.

Pennsylvania State University (Berks College, Reading). However, here we present results for onereference BR system with fixed concentrations of all components, except phenol, carried out in Belgrade,(University of Belgrade, Faculty of Physical Chemistry), unless otherwise stated. Experiments wereconducted in a thermostated, closed well-stirred reactor with the following initial formal concentrationsof reagents in the mixture: [HClO4]0¼ 0.10m, [KIO3]0¼ 0.020m, [MnSO4]0¼ 0.0020m, [MA]0¼ 0.016m,[H2O2]0¼ 1.2m. Temp. was always 25.08, and stirring rate s was 900 rpm. The volume of the reactionmixture in all experiments was 60 ml. The substances were added to the reaction vessel in the followingorder: phenol (50 ml), MAþMnSO4 (10 ml), KIO3þHClO4 (30 ml), and when the temp. reacted asteady value of 25� 0.18 and the potential was stabilized to � 0.2 mV, H2O2 (20 ml) was added (indifferent runs, the initial constant potential varied between 705 – 760 mV). The beginning of the reactionis defined as the moment when H2O2 was added to the vessel. A PC-Multilab EH4 16-bit analog-to-digitalconverter electrochemistry analyzer was directly connected to the reactor through a Pt working electrodeand a double junction Ag/AgCl electrode, and used to record the potential changes.

Comparable batch experiments have also been carried out in Bologna and Reading with similarapparatus and conditions and with similar results. Some experiments used iodide-sensitive electrodes.Minor differences in results can be attributed to different stirring rates and different order of addition.The exact number of oscillations and length of oscillation trains is subject to those and other yet unknownfactors [7].

CSTR Experiments. All experiments were carried out in a CSTR at 25� 0.18. The assembly iscomposed of a 50-ml glass CSTR vessel wrapped in a water-recirculation jacket connected to athermostat. For homogenization of the reaction mixture, a magnetic stirrer was used. Amounts of speciesin the reactor were controlled by peristaltic pumps. Four of the channels were used to deliver thereactants (aq. solns. of 1, KIO3/HClO4, 2, malonic acid (MA)/MnSO4, 3 H2O2, and 4 PhOH) and onechannel was used to remove the surplus volume of the reaction mixture through a U-shaped glass tube. Inthis way, the volume of the reaction mixture was kept constant at 22.2� 0.2 ml. The working Pt electrodewas connected to a double-junction Ag/AgCl reference electrode. An electrochemical device (PC-Multilab EH4 16-bit ADC) coupled with a personal computer was used to record the potential�timeevolution of the BR oscillator. The start-up procedure was performed in the following way. First,thermostated and protected from light, the reaction vessel was filled with the reactants, i.e., 0.020m KIO3,0.10m HClO4, 0.016m MA, 0.0020m MnSO4, 1.20m H2O2, and deionized water at the flow rate of 5 mlmin�1. After 1 min, the stirrer was turned to 900 rpm. After 2.5 min, the flow rate was set to 0.191 mlmin�1, and the other pump for removing the surplus volume of the reaction mixture was turned on. After30 min, deionized water was replaced with PhOH. [PhOH] was varied over the interval 4.6� 10�5

m<

[PhOH]0< 9.93� 10�5m.

Results and Discussion. – Open and Closed Reference Systems. Compared to thebeginning trace from the open reference system (CSTR; without phenol), the closed(batch) reference system undergoes gradual changes as the starting materials areexpended, and products accumulate. Shortly after oscillations end, the closed systemundergoes a transition from State I to State II (with solid I2 precipitation), due tosudden autocatalytic decomposition of accumulated I2(MA). In the open system, thistransition does not occur, because the precursor to I2(MA), I(MA), is maintained at alow level, being continually washed out. Hence, once the CSTR system comes to thesteady state regime, the flow of the reaction species in and out forces the system tobalance between its dynamical states throughout time. However, under some particularinitial conditions, the closed reactor evolves in time through the spectrum of dynamicalstates, eventually hitting the one similar to the open-reactor steady-state regime, butonly for a part of the time.

Batch System. This series of studies is related to a BR system which, in its basicstructure, a priori, contains PhOH. In other words, the BR system is perturbed at the


beginning of the reaction. Typical intermittences obtained under batch conditions inthe BR system are given in Fig. 2 for the case of [PhOH] of 2.20� 10�5

m.The reference BR system without PhOH is the same as reported in Fig. 1, a.

Comparison of Figs. 1,a, and 2 reveals several differences. Aside from the intermittentbursting phenomena, the amplitude in the PhOH system is smaller, and the total timewhere oscillations are observed is much longer. The sudden transition to high [I�] and[I2] in the reference system (solid I2 precipitates) is absent in the PhOH system. At theend of all oscillations, the PhOH system is colorless.

Intermittent-bursting BR systems can be described in various ways. For example,the numbers of oscillations per burst, and also the durations of both bursts and gapsbetween them, change consistently over time in each experiment (Table and Fig. 3).Precisely, bursts shorten with time and gaps are prolonged. The number of oscillationsper burst and the duration of the gaps both decrease with increasing [PhOH]0.

The induction periods (Tind), generally decrease with increasing [PhOH]0, althoughthere is some scattering between 3.2 and 3.6� 10�5

m (Table). In Fig. 2, we can see that,following addition of H2O2 to initiate oscillations, there is an initial rapid decrease in[I�] (increase in [HOI] and/or [HOIO]). The induction period follows, as [I�]gradually increases (seen with the I�-selective electrode). PhOH moderates theincrease in [HOI] and [HOIO], thus shortening the time to remove the excess.

The number of oscillations in the first burst as well as the duration of the first gapdepends on the initial concentration of PhOH (Fig. 4,a and b). The number ofoscillations has the maximum at approximately the same place where the duration ofthe first gap has the minimum. Moreover, the number of bursts, NB (Fig. 4,c), andaverage number of oscillations per burst, hNoi (Fig. 4,d), both first increase and thendecrease, as is the case with the number of oscillations in the first burst (Fig. 4, a). Zeropoints at both ends of graphs indicate that there are no bursts or gaps for thoseparameter values.


Fig. 2. Time series, potential vs. time, for BR mixture with [HClO4]0¼ 0.10m. [KIO3]0¼ 0.020m, [MA]0¼0.016m, [MnSO4]0¼ 0.0020m, [H2O2]0¼ 1.2m, [PhOH]0¼ 2.20� 10�5

m. Tfirst , Duration of the firstsequence of oscillations; Tind , induction period; TB, duration of burst; TG, duration of gap; TW, waiting

time, time which we waited after the last burst to confirm that sequence is really over.

Moreover, it is interesting to see the behavior of Tfirst in Fig. 5. With increasing[PhOH]0, the decreasing trend in Tfirst was noticed in all cases, even in those whenintermittences do not appear. The inflexion point associated with an autocatalyticeffect of PhOH appears when [PhOH] has the value corresponding to maxima andminima of other properties mentioned above.

In general, the durations for the bursts, TB, become progressively shorter, and thedurations of the gaps (TG) grow longer as each run proceeds (cf. Fig. 6).

The evolution of the BR system perturbed by PhOH can be described by the ratiobetween the total length of oscillations and the initial concentration of PhOH, [PhOH]0

(Fig. 7). Discontinuity of the relationships is observed in the domain of the PhOHconcentrations providing the appearance of the intermittences.

From Fig. 7, one can conclude that the intermittent-bursting behavior of the BRreaction is a kind of response of the system to the perturbation by PhOH. That is howthe oscillatory reaction expresses its tendency to maintain oscillations despite theaction of PhOH which tends to suppress it.

As mentioned before, the intermittent bursting occurs when two qualitativelydifferent behaviors replace one another randomly during the course of the reaction,although all the control parameters remain constant [11]. Varying the control


Table 1. Intermittences in the Batch BR System at Different Phenol Concentrations [PhOH]0. NB,Number of bursts; No, number of oscillations per burst; hNoi, the average number of oscillations per

burst; other abbreviations are the same as in Fig. 2.

[PhOH]0

[m� 10�5]Tind [min] NB No hNoi TB [min] TG [min] TW [min]

1.4 1.91 – – – – – 23.71.6 1.94 – – – – – 58.91.7 2.03 – – – – – 32.11.8 2.09 1 5 5 2.7 11.6 49.81.9 2.05 1 7 7 4.2 8.4 34,32.0 2.00 2 9, 6 7.5 5.6; 3.3 6.8; 9.8 34.22.2 2.39 4 10, 8, 6, 5 7.25 6.3; 4.9; 3.3; 2.7 6.2; 6.5; 9.0; 12.2 27.62.4 2.08 7 9, 8, 7, 6, 5, 5, 3 6.14 5.6; 4.8; 4.1; 3.3;

2.6; 2.6; 1.36.7; 7.0; 7,5; 8,5;8.6; 10.2; 23.0

45.7

2.5 2.04 7 9, 7, 7, 6, 5, 5, 3 6 5.6; 4.1; 4.1; 3.3;2.6; 2.6; 1.2

7.8; 7.3; 7.6; 8.8;9.3; 10.6; 22.3

27.7

2.8 1.88 7 9, 7, 6, 6, 5, 5, 4 6 5.7; 4.0; 3.3; 3.3;2.5; 2.6; 1.9

9.7; 9.9; 9.1; 9.6;11.4; 12.0; 20.8

33.0

3.0 1.55 5 7, 6, 5, 5, 4 5.4 4.2; 3.3; 2.5; 2.5; 1.8 11.5; 12.9; 12.9;14.2; 17.2

56.4

3.2 0.45 5 7, 6, 6, 5, 4 5.6 4.0; 3.2; 3.2; 2.4; 1.8 12.7; 13.5; 13.3;15.4; 17.0

32.1

3.4 1.75 5 6, 6, 5, 4, 4 5 3.4; 3.4; 2.6; 1.8; 1.8 13.6; 15.8; 17.9;17.0; 23.1

56.3

3.6 1.21 3 5, 5, 4 4.7 2.7; 2.7; 1.9 20.1; 25.6; 35.5 104.73.8 0.52 – – – – – 41.34.0 0.36 – – – – – 43.84.20 0.55 – – – – – 214

parameters of the considered system can change behaviors from permanently periodicto totally chaotic, passing through intermediate states. One possible measure of�distance� of the reaction system from regular periodic state is the ratio of the totalperiod that system spends in the new chaotically appearing states (sum of all TG) to thetotal period that system spends in the oscillatory state (Ttotal). In Fig. 8, this ratio ispresented as a function of [PhOH]0 as selected control parameter. The intercept withabscissa gives the critical value of [PhOH] necessary to shift the system from regularoscillatory state into the intermittent bursting state, i.e., the corresponding bifurcationpoint, [PhOH]c¼ (1.74 þ /� 0.17)� 10�5

m.Moreover, such kinds of systems can be also analyzed by other means. For example,

there is a relation between [PhOH]0 and the average frequency of oscillations for allbursts in one run, relation between the induction period and duration of the firstsequence oscillation, Tfirst , relation between the induction period and total oscillationlength, etc.

Experiments in Bologna confirmed that the intermittences appear in a range ofconcentrations of constituents that include [PhOH]0 between 3.0� 10�5

m and 4.4�


Fig. 3. Number of the oscillations per burst (a) and duration of the gaps (b) as a function of time for[PhOH]0 of a) 2.2 (*) , b) 2.4 (�) , and c) 3.2 (*) ,� 10�5

m. Other conditions were the same as in Fig. 2.

10�5m, [MA]0 between 0.016m and 0.0224m, [KIO3]0 from 0.020m to 0.040m, and

[H2O2]0 from 1.0m to 1.5m.In addition, the intermittences are not limited to MA and MnSO4 systems; batch

systems of [methylmalonic acid] from 0.031m to 0.056m (Reading) exhibitedintermittences and complex waveforms; CeIII-based systems ([CeIII]¼ 0.00040m,[PhOH]0¼ 2.9� 10�5

m to 4.8� 10�5m (Bologna), and ([CeIII]0¼ 0.0010m,

[PhOH]0¼ 5� 10�5m (Reading)) had very long total oscillation lengths (up to

180 min) including one to four bursts. The other concentrations were close to thoseof the reference system.


Fig. 4. The influence of the phenol concentration on a) the number of oscillations in the first burst (NB,1) ,b) the duration of first gap (TG,1) , c) the number of bursts (NB) , d) the average number of oscillations per

burst (hNoi). The conditions were the same as in Fig. 2.

Fig. 5. The influence of the phenol concentration on the duration of the first sequence of oscillations(Tfirst) . The conditions were the same as in Fig. 2.


Fig. 6. TB vs. the following TG for all the data compiled in the Table

Fig. 7. Relation between [PhOH]0 and total oscillations length, Ttotal , equal to the sum of all: Tfirst , TG, andTB

Two compounds closely related to PhOH were found (Reading) to produceintermittent bursts at concentrations close to 3� 10�5

m : 4-iodophenol and 4-bromophenol.

CSTR Results. By adding PhOH in various concentrations, we detected thesuppressing effect that PhOH has on the oscillatory dynamics of the BR oscillatingsystem. The effect can be detected as intermittent bursts. The extent of the oscillations�suppression is highly correlated with [PhOH] (Fig. 9). The reference BR systemwithout PhOH is the same as reported in Fig. 1,b.

Changing PhOH concentrations affects the time necessary for appearances of theintermittent bursts, the number of the oscillations in one cluster, the amplitude of thesmall noisy oscillations between two clusters, and whether or not intermittent burstscan be maintained steadily. Lower concentrations of the PhOH considered here allowkeeping the system permanently in the bursting state. Also, in that region, the timerequired for the system to reach the bursting state decreases with increasing [PhOH],as well as the number of the oscillations in bursts. Besides the effects mentioned above,amplitudes of the small oscillations between two clusters decrease. Higher phenolconcentrations prevent the system from being kept permanently in the bursting state.The time required for the system to reach intermittent bursts decreases as well as thenumber of the oscillations in one burst. This eventually leads to stable stationary states,which can be seen in Fig. 9,b. For [PhOH] of 9.93� 10�5

m and higher, the systemdirectly reaches a stable stationary state without manifestation of the intermittentbursts.


Fig. 8. The ratio between the total period, Ttotal , that the system spent in quiescent state (sum of all TG) andtotal period that the system spent in the oscillatory state (Ttotal , see legend of Fig. 7) as a function of the

phenol concentration. Bifurcation point is found at the intersection with abscissa.

Fig. 9, a, shows that, for the first 50 min or so, the reaction is still approaching astable oscillatory state, as the amplitude is decreasing somewhat. At ca. 50 min, PhOH(started at 30 min) begins to exert an effect. The upper potential in the oscillationsreaches a maximum at ca. 100 min. At ca. 130 min, the intermittences begin, and theamplitudes decrease slightly, and they are relatively stable after ca. 250 min. With aflow constant of ca. 0.0086 min�1, a few 100 min are required to reach a nearly stablestate in the open reactor.

With a higher [PhOH] input (Fig. 9,b), the reaction begins to show response toPhOH at ca. 45 min, and by ca. 77 min the oscillations cease, followed by a single burstca. 10 min later. At this time, the true level of [PhOH] in the reactor would still besignificantly less than 9.52� 10�5

m, so the upper limit of [PhOH], where intermittentbursts can be sustained, is lower than this value.

To verify that the intermittent bursting represents a stable state at low PhOHconcentrations in the CSTR, we present the results of an 18-h run in Fig. 10, whereintermittences began at ca. 3 h. For the last 8 h, the number of oscillations per burstsettled at 18� 1, and the interval between bursts was 6.3� 0.3 min. The intermittentbursting behavior is truly stabilized.


Fig. 9. Oscillatory dynamics of the BR reaction modified by phenol with inflow concentrations ofa) 5.03� 10�5

m and b) 9.52� 10�5m

In this experiment, besides packages (bursts) of oscillations with only large-amplitude oscillations, we also found few packages with small-amplitude oscillationsplaced between large-amplitude oscillations (Fig. 11).

Overall Comment. The comparison between the reference systems and systemsperturbed by PhOH is dramatic. In both closed and open systems, the PhOH-perturbedsystems exhibit lower amplitude and higher frequency, and after oscillations end, thereis a quiescent gap, followed by more oscillations. This sequence may repeat severaltimes, depending on PhOH concentration. Additionally, in the closed PhOH-perturbedsystem, the oscillations last longer, and there is no transition to State II. Thus, in theabove experiments, where the BR system with PhOH was considered, the intermittentbursts are obviously obtained under both batch and CSTR conditions. The intermittentbursts are very unusual phenomena that can be found in the reaction systems. Theybelong to the group of aperiodic oscillations, since the distances between bursts aresimilar but chaotic. It can be easily seen in the CSTR, since only in an open reactor isthe system truly in a steady state.

Fig. 11. Enlarged parts of Fig. 10 where small-amplitude oscillations are placed between large-amplitudeoscillations. As the length of the gaps between the bursts is chaotic, sometimes two bursts are nearly

connected.


Fig. 10. Long-time oscillatory dynamics of the BR reaction modified by phenol with an inflowconcentration of 5.53� 10�5

m

Phenol, without any doubt, reacts with the BR matrix (BR system without PhOH).The obvious question to be answered is �What is the mechanism of PhOH interaction?�.At least two types of reactions are known. In an acidic mixture of iodate and iodine,PhOH incorporates I2 to form successively mono-, di, and triiodinated phenol. Theactual addition reagent is HOI, which is also a key intermediate in the BR oscillator.2,4,6-Triiodophenol is quite insoluble, but has not been observed in oscillation mixtures(the amount would be small, and might easily be overlooked).

Besides addition reactions, PhOH is subject to oxidation, certainly to benzenetrioland further on to quinone. Phenol reacts with HOIO to give a product with anabsorbance peak at ca. 388 nm, which then slowly decays. The spectrum is very similarto that obtained from the reaction of catechol (1,2-dihydroxybenzene) with MnO2 orHOIO or IO�

3 , namely o-benzoquinone (cyclohexa-3,5-diene-1,2-dione) (Reading).This strongly suggests that, in the BR mixture, the phenol that is oxidized passesthrough catechol and on to o-benzoquinone and further. o-Benzoquinone slowlydecays to unknown polymeric products. It is known that catechol, above a certainminimum concentration, is a very effective inhibitor of BR oscillations [9c].

Thus, the behavior of the PhOH-perturbed BR oscillator is consistent with theabove-mentioned properties of PhOH. First, lower amplitudes would be expected,since PhOH reacts with two key intermediates, HOI and HOIO (and probably withHOO·). Second, the absence of a transition to State II is consistent with slowerproduction of IMA and I2MA due to lower amplitudes in the intermediates, I2, HOI,and HOIO. The decomposition of I2MA is autocatalytic in I2; if [I2] is low, autocatalysiswill be delayed. If autocatalysis is prevented, I2MA can decarboxylate to I2AA(CHI2COOH) [12]. Third, an assumption that remains to be tested is that the oxidationproducts of PhOH, catechol and benzoquinone, play a role in the intermittent behavior.Systems perturbed by catechol, o-benzoquinone, or p-benzoquinone (cyclohexa-2,5-diene-1,4-dione) exhibit very long times of oscillations, but no intermittences.

Although PhOH obviously reacts with BR matrix, the next question arises: is PhOHa species necessary to obtain intermittent bursting? As bursts were also found underbatch [13] and CSTR [14] conditions in the unperturbed Bray�Liebhafsky (acidiciodate, H2O2) reaction system, which is a subsystem of BR, we assume that PhOH is justthe trigger, which, by reacting with species in the BR matrix, shifts the system to anearby region of phase or parameter space with intermittent dynamics. Indeed, DeKepper et al. reported a very similar phenomenon in the BR system without PhOH, in aCSTR [15]. In this case, the trigger was the flow rate. �Bursting� was also found in theBelousov�Zhabotinsky oscillating reaction in a CSTR [16] [17] at a very particular flowrate.

Conclusions. – The intermittences are shown to be inherent to the reactionmechanism of the BR reaction. The phenomenon has been confirmed in threelaboratories around the world. Several different reagents and a wide interval ofconcentrations can be used to generate the intermittent bursts. Both closed- and open-reactor conditions are applicable. Moreover, the deterministic nature of the phenom-ena is further shown by consistent trends of several characteristic values with respect toPhOH concentration. Investigations are continuing with respect to the mechanismresponsible for the PhOH-induced phenomena.


This work was partially supported by the Ministry for Science of the Republic of Serbia (GrantsNos. 172015 and 45001).

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Received April 26, 2013


regularity of intermittent bursts in briggsrauscher oscillating systems with phenol

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