Control of the patterns by using time-delayed feedback near the codimension-three Turing–Hopf–Wave bifurcations

Control of the spatiotemporal patterns near the codimension-three Turing–Hopf–Wave bifurcations is studied by using time-delayed feedback in a three-variable Brusselator model. Linear stability analysis of the system shows that the competition among the Turing-, Hopf- and Wave-modes, the wavenumber, and the oscillation frequency of patterns can be controlled by changing the feedback parameters. The role of the feedback intensity Pu played on controlling the pattern competition is equivalent to that of Pw, but opposite to that of Pv. The role of the feedback intensity Pu played on controlling the wavenumber and oscillation frequency of patterns is equivalent to that of Pv, but opposite to that of Pw. When the intensities of feedback are applied equally, changing the delayed time could not alter the competition among these modes, however, it can control the oscillation frequency of patterns. The analytical results are verified by two-dimensional （2D） numerical simulations.     

Competition of Spatial and Temporal Instabilities underTime Delay near Codimension-Two Turing-Hopf Bifurcations

Competition of spatial and temporal instabilities under time delay near the codimension-two Turing-Hopf bifurcations is studied in a reaction-diffusion equation. The time delay changes remarkably the oscillation frequency, the intrinsic wave vector, and the intensities of both Turing and Hopf modes.
The application of appropriate time delay can control the competition between the Turing and Hopf modes. Analysis shows that individual or both feedbacks can realizethe control of the transformation between the Turing and Hopf patterns.Two-dimensional numerical simulations validate the analytical results.     

双层耦合介质中四边形图灵斑图的数值研究

采用双层线性耦合Lengyel-Epstein模型,在二维空间对简单正四边和超点阵四边形进行了数值分析.结果表明:当两子系统波数比N1时,随耦合强度的增大,基模的波矢空间共振形式发生改变,系统由简单六边形自发演化为结构复杂的新型斑图,除已报道的超六边形外,还获得了简单正四边和多种超点阵四边形,包括大小点、点线、白眼和环状超四边等斑图.当耦合系数α和β在一定范围内同步增大时,两子系统形成相同波长的Ⅰ型简单正四边;当α和β不同步增大时,由于两图灵模在短波子系统形成共振,系统斑图经相变发生Ⅰ型正四边→Ⅱ型正四边→超点阵四边形的转变;当系统失去耦合作用时,短波子系统波长为λ的Ⅰ型正四边斑图迅速失稳并形成波长为λ/N的Ⅰ型正四边,随模拟时间的延长,两子系统中不同波长的正四边均会经相变发生Ⅰ型正四边→Ⅱ型正四边→六边形的转变.     

反应扩散系统中反螺旋波与反靶波的数值研究

采用三变量Brusselator扩展模型在二维空间对反应扩散系统中反螺旋波和反靶波进行了数值模拟,利用色散关系和参量的时空变化研究了反螺旋波与反靶波的形成机制和时空特性,分析了方程参数对反螺旋波与反靶波的影响,获得了多种不同臂数的反螺旋波.模拟结果表明：反螺旋波源于波失稳、霍普失稳,或两种失稳的共同作用,而在反靶波中除上述两种失稳外还同时存在图灵失稳,波的传播方向均由外向内;反螺旋波波头的相位运动方向与波的走向相同,且旋转周期随臂数的增加逐渐增大;多臂数的反螺旋波由于受微扰及边界条件的影响,在波头的持续旋转运动中可以向臂数少的反螺旋波发生转变,并且在一定条件下单臂反螺旋波可实现到反靶波的转变;当不活跃中间物质的浓度的扩散系数超过临界值时,波的传播方向发生改变,系统可以实现反螺旋波到螺旋波以及反靶波到靶波的转变.     

时滞位移反馈对Helmholtz振子系统的分形侵蚀安全域的控制

对一个Helmoholtz振子系统引入线性时滞位移反馈,研究时滞位移反馈对系统的安全盆侵蚀的控制作用.将Melnikov函数法推广到时滞系统,从而给出时滞受控系统的安全盆的边界分形条件,在此基础上得出了安全盆分形的激励振幅阈值.再以时滞量为变参数,运用四阶Rung-Kutta方法和点映射方法从定量上研究了时滞对受控系统安全盆的影响规律.结果表明在弱反馈下,时滞量的增大能够提高安全盆边界分形的阈值,进而有效地抑制安全盆的分形侵蚀.说明时滞位移反馈是控制系统的安全盆侵蚀的良好方法. 关键词： 安全盆 分形侵蚀 时滞 反馈     

The nonequilibrium phase transition and the symmetry revival induced by time delay in an asymmetric bistable system with correlated noises

The nonequilibrium phase transition and the symmetry revival induced by time delay in a bistable system are investigated. The stationary probability distribution function (SPDF) of the bistable system with time delay and correlated noises are calculated by an analytical method and stochastic simulation respectively. The analytical and simulative results indicate that: (1) There is a certain value of λ (λ denotes the strength of correlations between the multiplicative and additive noises) to make the SPDF symmetric under some time delay; however, above or below the given value, the symmetry will be broken; (2) With the monotonic change of λ , the unimodal peak structure of SPDF becomes bimodal at the beginning, then it becomes unimodal again; this means that there is a reentrance phenomenon in the process; (3) There is a critical value of delay time, which makes the lower peak of SPDF equal to the higher one under the critical condition. This means that the symmetry revival phenomenon emerges.     

半周期延迟-非线性反馈控制混沌

提出了基于稳定性准则的半周期延迟-非线性反馈控制混沌的方法，即SC(stability criterion)半周期延迟非线性反馈控制法.通过对混沌系统的适当分离，得到一个特殊的非线性函数，并利用混沌输出信号与其半周期延迟信号的非线性函数之和，构造了连续反馈输入干扰.该方法继承了延迟反馈控制方法及稳定性准则控制方法的优点，实现了有效的自控制过程；并克服了延迟反馈方法的限制，能将嵌入混沌吸引子中的自对称直接不稳周期轨稳定.控制过程可随时开始，具有简便、灵活性.数值模拟结果显示了SC半周期延迟-非线性反馈方法控制的有效性. 关键词： 稳定性准则 混沌控制 半周期延迟 非线性反馈     

气体放电系统中时空斑图的时滞反馈控制

采用时滞反馈的方法实现了对气体放电半唯象模型中时空斑图的控制．在Turing—Hopf切空间附近分析了时滞反馈对Turing模与Hopf模的影响,确定了反馈参数与系统振荡频率及临界波长的关系．结果表明,在保持外加电压不变的情况下,时滞反馈可有效控制斑图的转换．增加反馈强度或延迟时间等效于增加外加电压．进一步利用二维数值模拟进行了验证．研究结果对气体放电系统中实现斑图的控制提供了一种新思路．     

利用OH自由基特征发射谱测量正庚烷的点火延迟时间

在化学激波管中利用反射激波进行点火,采用OH自由基在306.4nm处特征发射谱线强度的急剧变化标志燃料的着火,由光谱单色仪、光电倍增管、压力传感器和示波器组成测量系统,测量了正庚烷/氧气的点火延迟时间,点火压力(1.0±0.1)和(0.75±0.05)atm,点火温度1 170～1 730K,当量比1.0,得到了在此实验条件下正庚烷/氧气点火延迟时间随温度变化的关系式。研究结果表明正庚烷/氧气点火延迟时间随温度的增加呈指数减小,点火压力为0.75atm时,随着点火温度的增加,点火延迟时间的变化率要小于1.0atm条件时。实验结果为建立正庚烷燃烧反应动力学模型,验证正庚烷燃烧反应机理提供了实验依据。     

Delayed excitatory self-feedback-induced negative responses of complex neuronal bursting patterns

In traditional viewpoint, excitatory modulation always promotes neural firing activities. On contrary, the negative responses of complex bursting behaviors to excitatory self-feedback mediated by autapse with time delay are acquired in the present paper. Two representative bursting patterns which are identified respectively to be "Fold/Big Homoclinic"bursting and "Circle/Fold cycle" bursting with bifurcations are studied. For both burstings, excitatory modulation can induce less spikes per burst for suitable time delay and strength of the self-feedback/autapse, because the modulation can change the initial or termination phases of the burst. For the former bursting composed of quiescent state and burst, the mean firing frequency exhibits increase, due to that the quiescent state becomes much shorter than the burst. However, for the latter bursting pattern with more complex behavior which is depolarization block lying between burst and quiescent state, the firing frequency manifests decrease in a wide range of time delay and strength, because the duration of both depolarization block and quiescent state becomes long. Therefore, the decrease degree of spike number per burst is larger than that of the bursting period, which is the cause for the decrease of firing frequency. Such reduced bursting activity is explained with the relations between the bifurcation points of the fast subsystem and the bursting trajectory. The present paper provides novel examples of paradoxical phenomenon that the excitatory effect induces negative responses, which presents possible novel modulation measures and potential functions of excitatory self-feedback/autapse to reduce bursting activities.     

Pattern formation in the thiourea-iodate-sulfite system: Spatial bistability, waves, and stationary patterns

We present a detailed study of the reaction-diffusion patterns observed in the thiourea-iodate-sulfite (TuIS) reaction, operated in open one-side-fed reactors. Besides spatial bistability and spatio-temporal oscillatory dynamics, this proton autoactivated reaction shows stationary patterns, as a result of two back-to-back Turing bifurcations, in the presence of a low-mobility proton binding agent (sodium polyacrylate). This is the third aqueous solution system to produce stationary patterns and the second to do this through a Turing bifurcation. The stationary pattern forming capacities of the reaction are explored through a systematic design method, which is applicable to other bistable and oscillatory reactions. The spatio-temporal dynamics of this reaction is compared with that of the previous ferrocyanide-iodate-sulfite mixed Landolt system.     

利用自相关方法实现光脉冲时间延迟精确测量

为了满足在高精度波分复用/时分复用光采样系统中,采样光脉冲时间抖动低于100 fs的要求,开发了一套基于自相关法测量时间延迟的系统。通过光纤耦合器连接一路参考光路将光脉冲在时域上进行"复制",并使初始光脉冲和"复制"光脉冲相关,得到参考光路和被测光路的精确光程差,进而固定参考光路并接入不同被测光路从而得到多路被测光路之间相对延时。实验结果表明,利用自相关法测量脉冲时间间隔精度优于50 fs,满足波分复用/时分复用光采样系统研究需要。     

Deterministic and stochastic effects near the convective onset

The pure conduction state of a horizontal layer of fluid heated from below becomes unstable with respect to a convecting state when the temperature difference exceeds a critical value. We examine the question of how real, physical systems evolve from conduction to convection. Most experimental cells contain geometric or thermal inhomogeneities which render the bifurcation to convection imperfect. In that case the pure conduction state never exists and the convecting state evolves continuously and smoothly as the temperature difference is raised. When a sufficiently perfect experimental cell is constructed to eliminate this route to convection, then dynamic imperfections will usually prevail. When the temperature difference across the cell is raised, the vertical gradients in the sidewalls evolve at a rate which differs from that in the fluid. The resultingtransient horizontal thermal gradients initiate the convective flow. This phenomenon can be eliminated by providing sidewalls which have the same thermal diffusivity as that of the fluid. When that is done, the convective flow is started by random noise which exists in any experimental system. Analysis of experiments shows that the noise source is considerably stronger than thermal noise, but its origin is unclear at this time.     

Static and time-dependent properties of polymer gels around the volume phase transition

Recent progress in the study of the volume phase transition of polymer gels is reviewed. The phenomenological theories of swelling equilibrium and phase transition of gels are summarized, and some basic experimental results on poly-N-isopropylacrylamide (NIPA) gels are compared with the prediction from these theories. Special attention is paid to the elastic properties of the gel network near the volume phase transition. The effect of external stresses on the swelling and the phase transition is analyzed. Some anomalous and unique characteristics revealed in NIPA gels such as shape- and size-dependent swelling and phase transition properties, curious phase coexistence, and domain structure are presented. Experimental results on some time-dependent phenomena such as phase separation, spinodal decomposition, and pattern formation are also presented and discussed. Some problems inherent to gels from biological bodies are briefly discussed.     

Encryption and decryption using a sandwich phase diffuser made by using two speckle patterns and placed in the Fourier plane: Simulation results

In the present paper, we describe the encryption and decryption of two-dimensional images. The encryption is done by employing a sandwich phase diffuser made by using two elongated speckle patterns, and placed in the Fourier plane of a double random phase encoding system. After encryption, the two constituent phase diffusers of such a sandwich diffuser are separated. During decryption, if the conjugate of either of the two elongated phase speckle patterns is used, the image cannot be retrieved. Correct decryption is also not possible if a sandwich diffuser with any of the phase speckle patterns is shifted in position with respect to the other. For decryption, the encrypted image is Fourier transformed and multiplied by the conjugate of the sandwich diffuser, and then the product is further Fourier transformed. It is possible to generate the image only if both the elongated phase speckle patterns are matched point-to-point and then the proper conjugate is made. The use of elongated speckle patterns in constituting a sandwich phase diffuser makes the system less complicated as compared to the use of a sandwich diffuser made with normal speckle patterns, enabling an easy alignment of the random phase diffuser at the time of rejoining the constituent diffusers for making the right key. The ease of alignment is due to the reduction of the requirement of 360° scanning at the time of rejoining these diffusers with little reduction in the security of the system. Simulation results are presented in support of the proposed idea. For optical implementation, the decrypted image may be obtained by generating a phase conjugate wave by the phase conjugation technique, and passing through the same sandwich phase diffuser. To evaluate the reliability of the technique, mean square error (MSE) between the decrypted and original image has been calculated.     

Investigation of the Influence of Overvoltage,Auxiliary Glow Current and Relaxation Time on the Electrical Breakdown Time Delay Distributions in Neon

Results of the statistical analysis of the electrical breakdown time delay for neon‐filled tube at 13.3 mbar are presented in this paper. Experimental distributions of the breakdown time delay were established on the basis of 200 successive and independent measurements, for different overvoltages, relaxation times and auxiliary glows. Obtained experimental distributions deviate from usual exponential distribution. Breakdown time delay distributions are numerically generated, usingMonte‐Carlo method, as the compositions of the two independent random variables with an exponential and a Gaussian distribution. Theoretical breakdown time delay distribution is obtained from the convolution of the exponential and Gaussian distribution. Performed analysis shows that the crucial parameter that determines the complex structure of time delay is the overvoltage and if it is of the order of few percentage, then distribution of time delay must be treated as an convolution of two random variables. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

双色中红外激光场延迟及相位调控产生水窗区间光子

理论研究了双色中红外激光场时间延迟及相位对高次谐波光谱的影响.结果表明：当激光延迟为-1.0 fs,激光相位为0.2π和0时,谐波截止能量可以得到有效延伸,并且获得一个超宽水窗区间谐波连续平台区.此外,谐波光谱的延伸与控制场波长关系不大,即,在上述激光延迟和相位下,控制场波长在2300 nm到2700 nm区间时都可获得水窗区谐波光谱.最后,叠加光谱连续区的谐波可获得35 as的水窗区孤立阿秒脉冲.     

The role of defects in the transition between different symmetries in convective patterns

The properties of the transition between two patterns with different symmetries are studied in an experiment on thermal convection in a fluid layer heated from below. The defect structure is also analyzed and it is found that the unstable phase is present in the defect cores. The experimental results are in agreement with a model of three coupled Ginzburg-Landau equations.     

掺铒光纤中亚稳态粒子振荡和慢光时间延迟关系研究

由于光纤慢光在实际中的应用价值引起广泛关注. 技术手段上利用相干布居振荡效应实现光速可控更具有优势. 本文主要介绍了利用相干布居振荡效应 (CPO) 实现掺铒光纤中的光速减慢传输, 通过改变掺杂浓度、光纤长度、入射信号光及抽运光功率等参量, 具体研究了亚稳态粒子振荡和时间延迟的关系. 研究结果表明: 选择高浓度光纤、增加光纤长度、关闭抽运光源, 选择适当强度的信号光可以有效地增大时间延迟. 关键词： 掺铒光纤 时间延迟 相干布居振荡 慢光