线状铜电极在磷酸溶液中电流混沌振荡的同步行为

研究了恒电位下两个铜线电极在磷酸溶液中的电流混沌振荡行为,通过恒定不同的电位数值,改变单个电极的电流振荡混沌行为,研究了不同混沌间的相互作用.调整线电极间的距离,研究了电极间距对电流振荡行为的影响.实验中两电极的振荡间呈现了复杂的耦合作用,耦合后的频率与耦合前电极原有的频率不同.两电极的混沌电流振荡中呈现出同步、准周期同步和反相同步等现象.电极距离一定时,振荡波形差别很大的两电极的电流容易呈现反相同步和准周期同步,波形差别不大时容易产生同步.强的耦合导致电极间电流振荡的同步,电极距离的加大,电极间电流振荡难以产生同步.对耦合作用机制也进行了探讨.     

单向耦合Hindmarsh-Rose系统的同步

采用数值模拟方法, 研究了由两个具有不同初始条件单向耦合的Hindmarsh-Rose神经元所组成系统的动力学行为. 研究结果表明, 耦合强度对两个神经元的同步具有重要的影响. 当两个神经元的控制参数取值不同时, 即在驱动系统和响应系统均处于混沌态及驱动系统处于周期振荡态, 响应系统处于混沌态两种情况下, 随耦合强度的增加其放电活动都能从不同步达到相位同步, 最后实现近似完全同步.     

混沌系统的变量变化率反馈控制方法研究

设计了一种控制连续非线性系统中混沌的新方法--变量变化率脉冲反馈(VRPF)方法.介绍了VRPF方法的控制原理以及反馈系数和脉冲间隔的选择技巧.将此方法应用到BZ反应3D模型系统混沌的控制中,计算机仿真模拟显示,通过恰当地选择反馈系数和脉冲间隔,可以将系统稳定在1p、2p、3p、4p、…、2n×3mp (n、m为整数)这样不同的周期轨道,从而使系统的功率谱也由混沌态时的连续谱转变为具有分立单峰的分立谱.此外,仿真模拟还发现VRPF方法具有极宽的控制域.     

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。     

一种控制化学混沌的新方法--在全混沌区的非线性人工神经网络偶然微扰反馈控制

提出了一种控制化学混沌的新方法以稳定控制不稳定周期轨道 (UPO) .这是一种偶然比例反馈控制 (OPF)战略的扩展 ,它克服了OPF局限性 ,即OPF控制律的线性限制 ,并扩展到全混沌区 .本方法利用反传人工神经网络 (BP ANN)来表达非线性控制律 ,以增加控制的鲁棒性 .其有效性通过一个混沌自催化反应模型的数值模拟进行了检验 .     

Belousov-Zhabotinsky化学体系中超混沌及其同步的研究

曾有报道在Belousov-Zhabotinsky (BZ)体系的实验研究中未实现超混沌。但 通过不同类型的变量耦合方式,我们在该体系的Montanatar模型中得到了超混沌发 现无论采用何种耦合方式,只要耦合强度足够小,均能得到超混沌。另外,对两个 所产生的超混沌BZ体系,在全变量耦合、双变量耦合及K-B空间标量耦合法的策略 下,均实现了同步调制,并且从横截Lyapunov指数判据理论给予验证。探索了个别 状态变量在耦合中对同步所起的作用。通过双变量耦合发现[Ce~(4+)]不起作用; 通过K-B空间标量耦合法发现只有[Br~-]和[HBrO_2]的线性组合能起作用,可能由 于它们出现在同一个基元反应中。     

一种控制化学混沌的新方法

提出了一种控制化学混沌的新方法以稳定控制不稳定周期轨道(UPO).　这是一种偶然比例反馈控制(OPF)战略的扩展,它克服了OPF局限性,即OPF控制律的线性限制,并扩展到全混沌区.　本方法利用反传人工神经网络(BP-ANN)来表达非线性控制律,以增加控制的鲁棒性.　其有效性通过一个混沌自催化反应模型的数值模拟进行了检验.     

周期扰动位相对化学振荡的调制效应

由Rossler反应系统的理论模型出发,构造一种具有外部周期扰动的新动力学系统,并采用逆算符法和数值分析法研究该系统的振荡态在周期扰动调制下的动力学行为.结果表明,在周期扰动的调制下,系统的状态由单周期振荡态(1p)变为周期2(2p)、周期4(4p)等多周期振荡态以及混沌态.扰动位相是系统呈现上述多种演化模式的控制参数,在扰动位相不同的数值区间,系统呈现的演化模式不同,而且扰动位相数值的微小改变,还影响每种演化模式的内部结构.     

化学Lorenz模型中混沌的介观动力学

用系综模拟方法研究了化学Lorenz模型中混沌的介观动力学. 通过对主方程的随机模拟, 分析了盒频率(bin frequency)以及涨落和协方差在不同参数区的时间演化行为. 系综模拟分析在比通常宏观方程描述更为基本的层次上, 展示了确定性混沌的介观动力学图景. 对主方程也用累积展开法进行了分析.     

一混沌模型系综模拟研究

用随机模拟方法研究了化学混沌模型的介观动力学。对该混沌模型的系综模拟发现,在这种不稳定运动中存在强烈的内部涨落,然而由于混沌运动整体上的稳定性,使得系综中的代表点被限制在混沌吸引子上,并且单个代表点形成的随机轨道很好地保持了确定性混沌吸引子的基本特征。     

Feedback loops for Shil'nikov chaos: The peroxidase-oxidase reaction

Special structures in a chemical reaction network can give rise to bistability, oscillations, and chaos. It has been shown recently [A. Sensse and M. Eiswirth, J. Chem. Phys. 122, 044516 (2005)] that the introduction of an additional species in a supplementary feedback loop to a minimal autocatalytic oscillator gives rise to chaotic dynamics in a certain range of parameters, independent of the particular realization of the additional loop. This provides a possibility to decide if chaos may occur just by analyzing the network structure of an existing model. Here, we apply this concept to analyze the complex dynamics in several essential subsystems of the peroxidase-oxidase reaction system. The aim of the present paper is to determine the nature of the occurring chaos and its location in the parameter space by numerical bifurcation analysis and simulations.     

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.     

自催化三分子模型内噪声随机共振

The stochastic resonance in chemical reaction systems has recently attracted growing attentions. Using chemical Langevin equation,the effect of internal noise has been studied on the dynamical behavior of a single and a one-way coupled cubic autocatalator. For the single system,it is found that the internal noise can induce sustained oscillations,and the signal-to-noise ratio（SNR）undergoes a maximum with the variation of the system size. For the coupled system,the SNR passes through a maximum with changing coupling strengths as well as with changing system sizes,which demonstrates the occurrence of the internal noise stochastic resonance（INSR）and optimal size effect. In the presence or absence of influx into the system,the coupling enhanced or suppressed INSR is found in the coupled system. All cells of the coupled system appear to exhibit INSR at an approximately equal size at a suitable coupling strength,implying that the optimal system size and coupling strength can make the system reach an optimal chemical reaction state.     

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.     

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.     

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.     

Periodical forcing for the control of chaos in a chemical reaction

Control of the chaotic behavior of a chemical system can be achieved perturbing periodically some control parameters of the system. This procedure based on external forcing, which is based on the phenomenon of resonance, can change a chaotic behavior into a periodical one by means of the application of a sinusoidal perturbation. In this paper, the influence of a periodical modulation added to the parameter controlling the oxygen adsorption rate in a cellular automaton (CA) model studying CO oxidation is analyzed. This CA model considers the oxidation reaction of CO on a catalytic surface, taking into account the catalyst temperature variation in order to analyze the reaction time oscillatory behavior. Simulations of the CA model exhibit chaotic and quasiperiodical behaviors, and it can be shown that the periodical forcing strategy can suppress the chaotic dynamics by means of the stabilization of periodical solutions.     

Stern-Brocot trees in the periodicity of mixed-mode oscillations

We investigate the distribution of mixed-mode oscillations in the control parameter space for two paradigmatic chemical models: a three-variable fourteen-parameter model of the Belousov-Zhabotinsky reaction and a three-variable four-parameter autocatalator. For both systems, several high-resolution phase diagrams show that the number of spikes of their mixed-mode oscillations emerges consistently organized in a surprising and unexpected symmetrical way, forming Stern-Brocot trees. The Stern-Brocot tree is more general and contains the Farey tree as a subtree. We conjecture the Stern-Brocot hierarchical organization to be the archetypal skeleton underlying several systems displaying mixed-mode oscillations.     

Influence of metal ions on oscillatory behavior of zinc anode in nitric acid-potassium dichromate media

A zinc anode in acidic media is a new oscillatory electrochemical system which manifests interesting behaviors, from steady states to simple oscillations and chaos. This paper presents an experimental study of the influence of metal ions on the shape, amplitude and duration of the cell potential oscillations, and gives a qualitative explanation of the system’s behavior. A small quantity of Cu²⁺, Zn²⁺ or Fe³⁺ ions added to the system change dramatically the potential oscillations from chaotic behavior to simple oscillations. The method may be used for chaos attenuation.