Period-doubling and chaotic oscillations in the ferroin-catalyzed Belousov-Zhabotinsky reaction in a CSTR

The ferroin-catalyzed Belousov-Zhabotinsky(BZ) reaction,the oxidation of malonic acid by acidic bromate,is the most commonly investigated chemical system for understanding spatial pattern forma-tion. Various oscillatory behaviors were found from such as mixed-mode and simple period-doubling oscillations and chaos on both Pt electrode and Br-ISE at high flow rates to mixed-mode oscillations on Br-ISE only at low flow rates. The complex dynamic behaviors were qualitatively reproduced with a two-cycle coupling model proposed initially by Gy?rgyi and Field. This investigation offered a proper medium for studying pattern formation under complex temporal dynamics. In addition,it also shows that complex oscillations and chaos in the BZ reaction can be extended to other bromate-driven nonlinear reaction systems with different metal catalysts.     

甘草参与的B-Z振荡反应研究

以H+-Mn2+-BrO-3-CH3COCH3-甘草组成的化学振荡体系,应用电化学工作站记录电位(E)随时间(t)的变化,绘制化学振荡曲线.通过考察反应条件及反应物的浓度等因素对振荡曲线的影响,优化最佳的振荡反应条件,计算反应的活化能,推断反应的机理.为利用此方法鉴别中草药及研究中药治疗疾病提供理论依据.     

A new Belousov-Zhabotinsky reaction with fructose 1,6-bisphosphate as the organic substrate

The effects of temperature, free radicals, chloride and bromide ions, and bromine on the Belousov-Zhabotinsky reaction with fructose 1,6-bisphosphate were studied. The apparent activation energies of the induction period, lifetime, and oscillation period were found to be 76.24, 101.29, and 62.93 kJ mol⁻¹, respectively. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 906–908, May, 2006.     

Effects of delayed linear electrical perturbation of the Belousov-Zhabotinsky reaction: a case of complex mixed mode oscillations in a batch reactor

Delayed feedbacks are quite common in many physical and biological systems and in particular many physiological systems. Delay can cause a stable system to become unstable and vice versa. One of the well-studied non-biological chemical oscillators is the Belousov-Zhabotinskii (BZ) reaction. This gives relaxation oscillations for a considerable period of time under batch conditions. This paper deals with the effect of perturbing the limit cycle oscillation of BZ reaction by employing a delayed electrical feedback to the system under batch conditions. The parameters chosen to study are external resistance and delay. For various resistances and delays the system was electrically perturbed and found to exhibit various complex mixed mode oscillations. The dynamic features are accounted for by the Oregonator model, with time delay incorporated in one of the variables. This revised version was published online in June 2006 with corrections to the Cover Date.     

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

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.     

海洛因对别洛索夫-扎鲍京斯基振荡化学反应的影响及其分析应用

研究了海洛因对Belousov Zhabotinsky(B Z)振荡反应的影响 ,结果表明 :海洛因的加入明显地改变了振荡体系的周期和振幅 ,即对振荡体系产生扰动 ,扰动的浓度范围为 1.8× 10 -8～ 2 .1× 10 -3 mol/L ,且海洛因的浓度分别在 3.8× 10 -6～ 2 .8× 10 -5mol/L和 0 .9× 10 -6～ 2 .9× 10 -5mol/L范围内与振荡周期改变值ΔT和振幅改变值ΔA均呈现良好的线性关系 ,相关系数分别为 0 .9931和 0 .974 6。据此 ,建立了测定海洛因的新方法。     

Identification of two aromatic isomers between 3- and 4-hydroxy benzoic acid by their perturbation on the potential oscillations of a Belousov-Zhabotinsky system

A novel method for identification of two aromatic isomers of mono hydroxy benzoic acid (HBA) was reported by using their different perturbation effects on the potential oscillations of a Belousov-Zhabotinsky (BZ) system. In such a system, a macrocyclic complex of Cu [CuL](ClO₄)₂ was used as catalyst in which ligand L is 5,7,7,12,14,14-hexamethyl-1,4,8,11-tetraazacyclotetradeca-4,11-diene. To the BZ system, 3-hydroxy benzoic acid (3-HBA) could temporarily quench and regenerate potential oscillations with damping characters after inhibition time (t_in) while 4-hydroxy benzoic acid (4-HBA) could only change the oscillation amplitude (ΔA) to give damping oscillations with no inhibition time. Thus, these two isomers of HBA were identified. Reaction mechanisms of BZ have been proposed by FKN model. An explanation of perturbation mechanism is that, although 3-HBA reacted with BrO₂ while 4-HBA reacted with BrO₃⁻, they all produced 1,4-quinone.     

CSTR中H2O2-KSCN-CuSO4非线性反应体系的研究

非统性化学反应现象（包括化学振荡、化学波和化学混饨等）的研究近二十年来进展较快，BZ反应＊、NADH氧化的生化反应＊及卤类化合物主导的其它反应体系［’－’］的混饨、双节律等复杂非线性现象不断被发现并得到不同程度的确证．无卤无机反应体系的复杂非线性现象未见报导，我们选择H202－KSCN－CllS04－N。OH无卤体系K7］进行探索，此反应在连续搅拌反应器（CSTR）和封闭反应器（batch）皆有振荡现象，在体系中加入鲁米诺（11J．－－－－n由产生发光振荡现象问，我们对这个反应体系的进一步研究发现复杂振荡（包括非周期过程）…     

Chaos Synchronization in the Belousov-Zhabotinsky Chemical Reaction by Self-Adaptive Parameter Adjustment Scheme

Employing the self-adaptive parameter adjustment scheme, the chaotic dynamical behaviors in the coupled Belousove-Zhabotinsky-CSTR chemical system were investigated numerically. The confirmation of synchronization is using the criteria of maximum transverse Lyapunov exponent. The results show that when all the variables are involved in the parameter adjustment rule, the chaos synchronization between the response and the target systems were obtain. However, as only some of the variables can be detected easily in the real experiment, there are difficulties in employing this scheme experimentally. Therefore, that scheme to investigate the role of single variable separately were modified. The results show that no chaos synchronization can be obtained when Br- and HBrO2 are used separately, except when Ce4+ and BrMA are used. However, there is no easy way to detect BrMA in the experiment, Ce4+ becomes the unique feasible variable involved in the adjustment role. Besides, the synchronization efficiency of different combinations of stiff constant and damping constants has been studied by means of synchronization-arriving time.     

Chemical oscillations in the metal ion-catalyzed bromate-4-aminophenol reaction

Temporal oscillations of the bromate-4-aminophenol system have been studied in the presence of four different catalysts:tris(1,10-phenanthroline)iron(II) sulfate(ferroin),Ce(III),Mn(II),and Fe(II).Transient temporal oscillations were observed in the four catalyzed systems when the reactions were conducted in a stirred batch reactor.The induction time was prolonged by the presence of ferroin,but it was shortened in the Ce(III)-and Mn(II)-catalyzed systems.On the other hand,the number of peaks was significantly decreased in the presence of ferroin.The development of oscillatory behaviour was found to be more sensitive to the ratio of bromate and 4-aminophenol concentration than to their absolute concentrations.The reaction rates of 4-aminophenol with Ce(IV) and 4-aminophenol with ferritin were measured directly by spectroscopic methods in a sulfuric acid medium.     

Simulation of noise characteristic effects on stochastic resonance in Belousov-Zhabotinsky flow reaction

A three-variable model, which was proposed to account for the stochastic resonance (SR) in Belousov-Zhabotinsky (B-Z) reaction in a continuous-flow stirred-tank reactor, is investigated when the control parameter kr, the flow rate, is modulated by noise near supercritical Hopf bifurcation point. Using the computer simulation, noise-induced oscillations are observed, and the signal-to-noise ratio (SNR) goes through a maximum with the increment of noise intensity, which means occurrence of stochastic resonance. in addition, we have also investigated the effects of correlation time of colored noise and the duration time of white noise on the system's dynamics.     

Pentanary cross-diffusion in water-in-oil microemulsions loaded with two components of the Belousov-Zhabotinsky reaction

We measure cross-diffusion coefficients in a five-component system, an aerosol OT (AOT) water-in-oil microemulsion loaded with two constituents of the Belousov-Zhabotinsky (BZ) reaction (H(2) O/AOT/BZ1/BZ2/octane). The species BZ1 is either NaBr, an inhibitor of the BZ reaction, or ferroin, a catalyst for the reaction. As species BZ2, we choose Br(2) , an intermediate in the reaction. The cross-diffusion coefficients between BZ1 and BZ2 are found to be negative, which can be understood in terms of complexation between these species. Using a four-variable model for the BZ reaction, we find that the cross-diffusion coefficients measured here can lead to a noticeable shift in the onset of Turing instability in the BZ-AOT system.     

Diffusion-controlled instabilities and stationary structures in a model for a ferroin-catalyzed Belousov-Zhabotinskii reaction

A model for the bromate-ferroin-bromomalonic acid reaction has been used to examine the conditions under which the homogeneous state loses stability as a result of Turing bifurcation. Stationary periodic structures with small or large amplitudes can exist. There is also a structure modification effect.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 24, No. 4, pp. 440–449, July–August, 1988.I am indebted to A. M. Zhabotinskii and Yu. A. Kuznetsov for useful discussions, and also to I. I. Goryanin for providing access to his software suite for defining a curve in n-dimensional space.     

pH oscillations in the BrO3--SO3(2-)/HSO3- reaction in a CSTR

Large-amplitude pH oscillations have been measured during the oxidation of sulfur (IV) species by the bromate ion in aqueous solution in a continuous-flow stirred tank reactor in the absence of any additional oxidizing or reducing reagent. The source of the oscillation in this simple chemical reaction is a two-way oxidation of sulfur (IV) by the bromate ion: (1) the hydrogen-ion-producing self-accelerating oxidation to sulfur (VI) (SO4(2-)), and (2) a hydrogen-ion-consuming oxidation to sulfur (V) (S2O6(2-)). In such a way, both the H+-producing and H+-consuming composite processes required for a pH oscillator take place in parallel in a reaction between two reagents in this system. A simple reaction scheme, consisting of the protonation equilibria of SO3(2-) and HSO3-, the oxidation of HSO3- and H2SO3 by BrO3- to SO4(2-), and the oxidation of H2SO3 to S2O6(2-) has successfully been used to simulate the observed dynamical behavior. Simulation with this simple scheme shows that oscillations can be calculated even if only about 1% of sulfur (IV) is oxidized to S2O6(2-) along with the main product SO4(2-). Agreement between calculated and measured dynamical behavior is found to be quite good. Increasing temperature decreases both the period length of oscillations in a CSTR and the Landolt time measured in a closed reactor. No temperature compensation of the oscillatory frequency is found in this reaction.     

Complex dynamics and enhanced photosensitivity in a modified Belousov-Zhabotinsky reaction

This study presents an experimental investigation of nonlinear dynamics in a modified Belousov-Zhabotinsky (BZ) reaction, in which the addition of 1,4-benzoquinone induced various complex behaviors such as mixed-mode oscillations and consecutive period-adding bifurcations. In addition, the presence of 1,4-benzoquinone significantly enhanced the photosensitivity of the ferroin-catalyzed BZ system, in which light-induced transitions between simple and complex oscillations have been achieved. Mechanistic study suggests that the influence of benzoquinone may arise from its interactions with the metal catalyst ferroin/ferriin, where cyclic voltammograms illustrate that the presence of benzoquinone causes an increase in the redox potential of ferroin/ferriin couple, which may consequently alternate the oxidation and reduction paths of the catalyst.     

Quantitative investigation of spatiotemporal chaos in the ferroin-catalyzed Belousov-Zhabotinskii reaction in a batch reactor

We have analyzed experimental data on the time dependence of the potentials of 16 platinum point-contact electrodes for spatiotemporal chaos in the Belousov-Zhabotinskii reaction. We show that the largest Lyapunov exponent is a convenient characteristic for spatiotemporal chaos. We found that in going from temporal to spatiotemporal chaos, the embedding dimension of the system increases by a factor of three. We have observed that as the largest Lyapunov exponent increases, we observe a decrease in the degree of spatial correlation of the process.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 31, No. 1, pp. 34–39, January–February, 1995.We would like to thank the Foundation for Basic Research of the State Science and Technology Committee of Ukraine for financial support of this work (Project 3.3/87).     

实验控制Belousov-Zhabotinsky-CSTR化学混沌反应

用两种方法来控制在连续流动釜式反应器(CSTR)中的Belousov-Zhabotinsky(BZ)化学混沌反应:(1)自适应延迟时间反馈控制方案;(2)线性自相互作用控制方案。第一种控制方案是一种微扰控制,并能将BZ-CSTR化学混沌稳定控制到其内嵌的不稳定周期轨道(UPO)上去。这种方法的优越之外可以由系统延迟时间的自适应调节得以显示。第二种控制方案可以驱动BZ-CSTR混沌动力学到达一系列规则的动力学状态,这些动力学状态可能并不是混沌轨道中内嵌的本征轨道。在控制BZ-CSTR化学混沌反应的实验中,这两种方案显示出了很大的灵活性和有效性。     

Discontinuously propagating waves in the bathoferroin-catalyzed Belousov-Zhabotinsky reaction incorporated into a microemulsion

Three new types of discontinuously propagating waves are reported in the bathoferroin-catalyzed Belousov-Zhabotinsky (BZ) reaction dispersed in water-in-oil Aerosol OT microemulsion. Jumping waves (JWs) are typically observed at or above room temperature and develop from the familiar trigger waves. Bubble waves (BWs) typically emerge from trigger or JWs at similar temperatures, while rotating waves (RWs) evolve from JW at higher temperatures (>40 degrees C). All these waves propagate discontinuously in a saltatory fashion. Other characteristic features include a discontinuous front for BW consisting of small concentric waves (bubbles) and lateral rotation of annular RWs. All three types of waves, as well as segmented but continuously propagating waves, can coexist. A simple model that is able to describe both jumping and segmented waves is described.     

Bromide control, bifurcation and activation in the Belousov-Zhabotinsky reaction

The unstirred, ferroin (Fe(phen)3(2+)) catalyzed Belousov-Zhabotinsky (BZ) reaction is the prototype oscillatory chemical system. Reaction media with added Br(-) appear red (reduced, low [Fe(phen)3(3+)]) during an induction period of several minutes, followed by the "spontaneous" formation of "pacemaker" sites, which oscillate between a blue, oxidized state (high [Fe(phen)3(3+)]) and the red, reduced state and generate target patterns of concentric, outwardly moving waves of oxidation (blue). Auto-oscillatory behavior is also seen in the Oregonator model of Field, Koros and Noyes (FKN), a robust, reduced model that captures qualitative BZ kinetics in the auto-oscillatory regime. However, the Oregonator model predicts a blue (oxidized) induction phase. Here we develop a generalized Oregonator-like model with no explicit bifurcation parameter that yields the observed transition from a red initial state to oscillatory dynamics, and displays a new bifurcation mechanism not seen in the original Oregonator.     

The Revival Wave Induced Spontaneously in a BZ-Type Mixture

We have examined the unusual behavior of wave propagation in the BrO₃ ^- - 1,4- cyclohexanedione - ferroin reaction system. Two patterns of traveling wave have been induced spontaneously with long time lag in the reaction process. A new wave has been induced as a concentric pattern after an initially induced wave has disappeared. The initially induced wave shows an irregular spiral pattern with a high wave frequency. The two waves show very different behavior in the pattern and in other wave characteristics as well. We compared the behavior of the two waves and suggested an appropriate reaction process for unusual behavior of wave propagation in the system by considering the reaction intermediates of the organic compounds. This revised version was published online in June 2006 with corrections to the Cover Date.