Period-doubling and chaotic oscillations 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 formation. 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 Iow flow rates. The complex dynamic behaviors were qualitatively reproduced with a two-cycle coupling model proposed initially by Gy(o)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.     

Periodic, Mixed-Mode, and Chaotic Regimes in the Belousov–Zhabotinskii Reaction Catalyzed by Ferroin

The periodic, mixed-mode, and chaotic regimes in the ferroin-catalyzed Belousov–Zhabotinskii (BZ) reaction observed in a continuous stirred tank reactor (CSTR) reactor at various flow rates were experimentally studied. It was found that an increase in the flow rate resulted in the appearance of various complex oscillations. The possibility of the numerical simulation of experimentally observed asymptotic mixed-mode oscillations and chaotic regimes with the use of a kinetic scheme that includes experimental rate constants of each step of the ferroin-catalyzed BZ reaction was first demonstrated. The reaction scheme adequately describes the bifurcation sequence of experimentally observed oscillating regimes.     

Complex and chaotic oscillations in a model for the catalytic hydrogen peroxide decomposition under open reactor conditions

Numerous periodic and aperiodic dynamic states obtained in a model for hydrogen peroxide decomposition in the presence of iodate and hydrogen ions (the Bray-Liebhafsky reaction) realized in an open reactor (CSTR), where the flow rate was the control parameter, have been investigated numerically. Between two Hopf bifurcation points, different simple and complex oscillations and different routes to chaos were observed. In the region of the mixed-mode evolution of the system, the transitions between two successive mixed-mode simple states are realized by period-doubling of the initial state leading to a chaotic window in which the next dynamic state emerges mixed with the initial one. It appears in increasing proportions in concatenated patterns until total domination. Thus, with increasing flow rate the period-doubling route to chaos was obtained, whereas with decreasing flow rate the peak-adding route to chaos was obtained. Moreover, in very narrow regions of flow rates, chaotic mixtures of mixed-mode patterns were observed. This evolution of patterns repeats until the end of the mixed-mode region at high flow rates that corresponds to chaotic mixtures of one large and many small amplitude oscillations. Starting from the reverse Hopf bifurcation point and decreasing the flow rate, simple small amplitude sinusoidal oscillations were encountered and then the period-doubling route to chaos. With a further decreasing flow rate, the mixed-mode oscillations emerge inside the chaotic window.     

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.     

过氧化氢氧化硫化钠反应体系的复杂振荡

研究了过氧化氢和硫化钠反应体系在连续流动搅拌反应器中的复杂振荡行为. 观察到11型振荡、12型振荡、非周期振荡以及衰减振荡; 在振荡周期内, 拐点附近区域H+扰动产生的延迟与振荡相位pH有关. 在完全基于硫价态变化的经验速率方程模型的基础上进行数值模拟, 得到的各种复杂振荡行为与实验现象基本一致, 证明了硫价态变化可驱动复杂非线性动力学行为.     

Structures of chaos in open reaction systems

By numerically simulating the Bray-Liebhafsky (BL) reaction (the hydrogen peroxide decomposition in the presence of hydrogen and iodate ions) in a continuously fed well stirred tank reactor (CSTR), we find "structured" types of chaos emerging in regular order with respect to flow rate as the control parameter. These chaotic "structures" appear between each two successive periodic states, and have forms and evolution resembling to the neighboring periodic dynamics. More precisely, in the transition from period-doubling route to chaos to the arising periodic mixture of different mixed-mode oscillations, we are able to recognize and qualitatively and quantitatively distinguish the sequence of "period-doubling" chaos and chaos consisted of mixed-mode oscillations (the "mixed-mode structured" chaos), both appearing in regular order between succeeding periodic states. Additionally, between these types of chaos, the chaos without such recognizable "structures" ("unstructured" chaos) is also distinguished. Furthermore, all transitions between two successive periodic states are realized through bifurcation of chaotic states. This scenario is a universal feature throughout the whole mixed-mode region, as well as throughout other mixed-mode regions obtained under different initial conditions.     

Transient complex oscillations in a closed chemical system with coupled autocatalysis

In this study, hydroquinone was introduced to the classic Belousov-Zhabotinsky (BZ) reaction to build up coupled autocatalytic feedbacks. Various complex dynamical behaviors including successive period-adding bifurcations, irregular oscillations, and frequency modulations were observed in the coupled reaction system. Not only the complexity of oscillations but also the time period during which complex oscillations persist were found to depend greatly on the initial concentration of hydroquinone, which was expected to manifest the coupling strength in the studied system. Dependence of the observed transient complex oscillations on concentrations of ferroin, sulfuric acid, bromate, and malonic acid was also characterized systematically. Numerical simulations with a modified BZ model via incorporating reactions involving hydroquinone and products of hydroquinone qualitatively reproduced the influence of hydroquinone seen in experiments.     

Determination of gases (NO, CO, Cl(2)) using mixed-mode regimes in the Belousov-Zhabotinskii oscillating chemical reaction

We show a principle possibility of the determination of gases concentrations (NO, CO, Cl(2)) by their affect on mixed-mode oscillations in the Belousov-Zhabotinskii (BZ) oscillating chemical reaction. These oscillations are characterized by single large amplitude oscillation followed by a number of small amplitude oscillations. The method of the determination is based on a construction of a calibration plot given by the dependence of the number of small amplitude oscillations on gas concentration.     

Conditions for Mixed Mode Oscillations and Deterministic Chaos in Nonlinear Chemical Systems

An approach has been proposed for finding the conditions for the existence of mixed-mode oscillations and deterministic chaos in a kinetic scheme after reduction to a simple system of equations. Analysis of the position and stability of the steady states of this system suggested simple conditions for the existence of mixed-mode oscillations and deterministic chaos. The boundaries for monostability, bistability, and oscillations were also found. The results obtained were completely confirmed by numerical modelling.     

The state space of a model for the Bray-Liebhafsky oscillating reaction

It has been known for a long time that the decomposition of hydrogen peroxide catalyzed by hydrogen and iodate ions, the Bray-Liebhafsky reaction, can generate oscillations in a batch reactor. Recently, mixed-mode oscillations and chaos have also been observed in a CSTR. The model we had previously proposed to explain the kinetics in a batch reactor can also simulate these new complex behaviors. Time series give only a limited view of the features of the calculated behaviors and more information is obtained studying the properties of the state space. We use projections of the trajectories, calculation of the correlation dimension of the attractor, Poincaré sections, and return maps. As the state space of the model is six-dimensional, we try to answer the questions of whether the projections into a 3D subspace give correct pictures of the real trajectories and whether we have reasons to prefer a special subspace. The text was submitted by the authors in English.     

亚氯酸盐-硫代硫酸盐非缓冲体系的动力学

研究了亚氯酸盐-硫代硫酸盐反应体系在非缓冲条件下的复杂动力学行为.结果发现,在开放体系中反应的pH值和Pt电位存在准周期振荡分叉和混合模式振荡分叉通向混沌的过程，且pH峰与Pt电位峰反相位.当与起始浓度比相对较小时，随着流速的逐渐升高，体系的pH值和Pt电位从简单的小振幅振荡(S)经过准周期振荡分叉到混沌，最后回到简单大振幅振荡(L)；而当与起始浓度比相对较高时，随着流速的降低，体系的pH值和Pt电位出现LS1、LS2、LS3…LSn的混合模式振荡,并在每对(LSn、LSn＋1)振荡区间发现了LSn、LSn＋1随机出现的非周期振荡行为.运用硫价态变化的一般动力学模型，模拟出了反应体系的混合模式振荡及非周期振荡.     

Analysis of complex oscillatory dynamics of a pH oscillator

Reaction systems that display pronounced periodic and aperiodic variations in the pH value of the reaction medium are known as pH oscillators. A member of this family of reactions studied here, the Cu(II)-catalyzed oxidation of thiosulfate by hydrogen peroxide in acidic solution, is known to display a rich variety of oscillatory dynamics. We focus on experimental time series showing complex aperiodic dynamics that simultaneously possesses the characteristics of period-doubled large-amplitude oscillations and irregular small-amplitude oscillations reminiscent of mixed-mode dynamics. An analysis based on the reconstruction of the attractor from the measured time series by two different methods and subsequent calculation of the maximal Lyapunov exponent reveals that this interesting dynamical regime is a manifestation of deterministic chaos. The text was submitted by the authors in English.     

Temperature-induced route to chaos in the H2O2-HSO3(-)-S2O3(2-) flow reaction system

Low-frequency, high-amplitude pH-oscillations observed experimentally in the H2O2-HSO3(-)-S2O3(-) flow reaction system at 21.0 degrees C undergo period-doubling cascades to chemical chaos upon decreasing the temperature to 19.0 degrees C in small steps. Period-4 oscillations are observed at 20.0 degrees C and can be calculated on the basis of a simple model. A reverse transition from chaos to high-frequency limit cycle oscillations is also observable in the reaction system upon decreasing further the temperature step by step to 15.0 degrees C. Period-2 oscillations are measured at 18.0 degrees C. Such a temperature-change-induced transition between periodic and chaotic oscillatory states can be understood by taking into account the different effects of temperature on the rates of composite reactions in the oscillatory system. Small differences in the activation energies of the composite reactions are responsible for the observed transitions. Temperature-change-induced period doubling is suggested as a simple tool for determining whether an experimentally observed random behavior in chemical systems is of deterministic origin or due to experimental noise.     

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.     

光敏性BZ反应的时空动力学

作为研究非线性时空动力学最理想的化学反应体系之一,三联(2,2'-联吡啶)钌(Ⅱ)(Ru(bpy)₃²⁺)为催化剂的Belousov-Zhabotinsky (BZ)振荡反应具有独特的光敏特性并能呈现丰富的时空动力学行为。研究光控BZ反应有助于我们对一系列物理、化学和生命体系中复杂动力学现象的理解。本文综述了不同实验条件下光效应对钌催化BZ反应均相复杂振荡和空间反应扩散化学波的影响, 以及光响应BZ反应与软物质耦合体系的复杂动力学行为,在此基础上介绍光抑制和光诱导反应机理和模型。对光控BZ反应体系存在的问题和发展方向进行了探讨。     

Dependence of turbidity oscillations of self-oscillating polymers on the selective recognition of the crown ether receptors contained in the polymer chain

The turbidity oscillations of self-oscillating polymers in the Belousov-Zhabotinsky (BZ) reaction system depending on the crown ether receptors contained in the polymer network have been studied. The three monomers are copolymerized, namely, N-isopropylacrylamide, the metal catalyst monomer for the BZ reaction, and the crown ether receptor monomer, to prepare the self-oscillating polymers used in this study. The turbidity oscillations are characterized by monitoring the transmittance of the polymer solution in the BZ reaction system at a specific wavelength of 570 nm. The oscillations are varied by crown ether receptors used in the polymerization process, i.e., BCAm(6) or BCAm(5), for the selective recognition of specific cations between potassium and sodium ions in the solution. The selective recognition of the BCAm receptors in the polymer chain for the two ions has brought out a variation in the turbidity oscillations by a change in the hydrophilicity of the polymer chain. The oscillations of the polymer solution composed of the BCAm(5) receptor are more influenced by sodium ion, while the polymer solution of BCAm(6) receptor is affected by potassium ion. However, the oscillation patterns of the redox changes obtained by these solution systems look much alike despite the differences in the polymer chain by crown ether receptors and cations of bromate used for the BZ reaction.     

Several types of oscillations in Belousov–Zhabotinskii reactions with amino acids as organic substrates

Under batch‐reactor conditions, 7 amino acids were employed as organic substrates in Belousov–Zhabotinskii (BZ) oscillations. These amino acids displayed different types of oscillations. Aspartic acid exhibited the classical BZ oscillations owing to the formation of oxalacetic acid (an intermediate of Aspartic acid oxidation) which is easily brominated. Tyrosine exhibited the uncatalyzed BZ oscillations where the metal ion catalyst is not necessary. Cystine, alanine, glycine, and glutamic acid could give rise to sustained oscillations only in the presence of acetone as a coupled organic substrate to remove bromine via bromination, known as the mixed‐substrate BZ oscillations. Serine showed oscillations even in the absence of acetone though serine is not subjected to bromination. Obviously, this is a new kind of BZ type oscillations since no bromination occurred at all. The excess bromine is possibly removed through the reduction by serine and/or its intermediates. Addition of acetone induces the dual‐frequency oscillations. © 2002 Wiley Periodicals, Inc. Int J Chem Kinet 34: 405–410, 2002     

Oscillatory behavior in the electrochemical oxidation of formic acid on Pt(100): rotation and temperature effects

We investigated the oscillatory behavior in the kinetics of formic acid electrooxidation on Pt(100) in 1 mM HClO₄ solution. We studied the effect of different experimental parameters on the oscillatory behavior, viz. defined HCOOH mass-transport to the electrode surface by using the rotating disk electrode technique, the temperature of the supporting electrolyte, and the nature of anions. We suggest that the interdependence of the reaction steps during HCOOH oxidation, the adsorption of anions and the competition for adsorption sites among the reaction partners and intermediates lead to complex non-linear kinetics. It was evident that once the individual reactions in the dual path mechanism reach steady state the oscillations vanish. These conditions can be reached either by enhanced formic acid reaction rates induced by electrode rotation or by increased temperature. Under specific conditions of anion and formic acid concentration, relaxational oscillations can be transformed into mixed-mode oscillations.     

Flow-induced control of chemical turbulence

We report spatiotemporal chaos in the Oregonator model of the Belousov-Zhabotinsky reaction. Spatiotemporal chaos spontaneously develops in a regime, where the underlying local dynamics show stable limit cycle oscillations (diffusion-induced turbulence). We show that spatiotemporal chaos can be suppressed by a unidirectional flow in the system. With increasing flow velocity, we observe a transition scenario from spatiotemporal chaos via a regime of travelling waves to a stationary steady state. At large flow velocities, we recover the known regime of flow distributed oscillations.     

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.