Determination of parameters of elements and coupling architecture in ensembles of coupled time-delay systems from their time series

We propose a method for reconstructing model differential equations with time delay for ensembles of coupled time-delay systems from their time series. The method has made it possible to recover the parameters of elements of the ensemble as well as the architecture and strength of couplings in ensembles of nonidentical systems with delay with an arbitrary number of unidirectional and bidirectional couplings between them. The effectiveness of the method is demonstrated for chaotic and periodic time series of model equations for ensembles of diffusively coupled systems with time delay in the presence of noise, as well as experimental time series for resistively coupled radiotechnical oscillators with delayed feedback.     

Recovery of delay time from time series based on the nearest neighbor method

We propose a method for the recovery of delay time from time series of time-delay systems. The method is based on the nearest neighbor analysis. The method allows one to reconstruct delays in various classes of time-delay systems including systems of high order, systems with several coexisting delays, and nonscalar time-delay systems. It can be applied to time series heavily corrupted by additive and dynamical noise.     

Recovery of parameters of delayed-feedback systems from chaotic time series

Methods for reconstructing a delay differential equation from the time series of an observable quantity are proposed for various classes of time-delay systems. The methods rely on knowledge of the distributions of extrema of the time series of observed oscillations and projection of the infinite-dimensional phase spaces of time-delay systems onto special low-dimensional subspaces. The effectiveness of the proposed methods is demonstrated by reconstructing delay differential equations from their chaotic solutions, including those corrupted by noise, and by constructing models of real time-delay systems from chaotic time series.     

时滞复Lorenz混沌系统特性及其自时滞同步

自时滞同步是指保持混沌系统结构和参数不变的情况下, 使时滞系统和原系统同步, 从而避免了现实中因为时滞而产生的各种问题. 本文以时滞复Lorenz系统为例, 研究其动态特性及时滞因数的影响, 并提出了一种非线性反馈控制器实现了复Lorenz系统的自时滞混沌同步. 数值仿真结果验证了该控制器的有效性. 该控制器只对部分状态进行控制, 实现了所有状态的同步, 原理简单, 易于工程实现. 关键词： 时滞系统 复混沌系统 自时滞同步 Lyapunov指数     

Stochastic resonance in two kinds of asymmetric nonlinear systems with time-delayed feedback and subject to additive colored noise

This paper attempts to investigate the stochastic resonance (SR) behaviors in two kinds of asymmetric nonlinear systems with time-delayed feedback driven by additive colored noise by virtue of two-state theory, small time delay approximation, path integral approach, and unified colored-noise approximation, where asymmetric nonlinear systems include asymmetric well depth and asymmetric well width alone. The characteristics of SR in two kinds of asymmetric systems are different for different asymmetric ratios and correlated times of additive colored noise. For asymmetric well width, optimal noise intensity is independent of asymmetric ratio and correlated time, whereas for asymmetric well depth it is closely related with asymmetric ratio and correlated time. However, optimal noise intensity is closely related with feedback intensity, and time-delay for two kinds of asymmetries. Even there exists the optimal feedback intensity, time delay and correlated time to make output SNR maximum. Above clues are helpful to achieve weak signal detection under strong background noise.     

Parameter estimation for chaotic systems with and without noise using differential evolution-based method

We present an approach in which the differential evolution (DE) algorithm is used to address identification problems in chaotic systems with or without delay terms. Unlike existing considerations, the scheme is able to simultaneously extract (i) the commonly considered parameters, (ii) the delay, and (iii) the initial state. The main goal is to present and verify the robustness against the common white Guassian noise of the DE-based method. Results of the time-delay logistic system, the Mackey-Glass system and the Lorenz system are also presented.     

随机基因选择模型中的延迟效应

研究了噪声驱动的基因选择模型中的延迟效应. 据小延迟方法和随机等价法则得到相应的延迟Fokker-Planck方程, 给出稳态概率分布函数的近似表达式. 分析了在噪声驱动下, 延迟时间对系统稳态性质的影响. 结果表明: 延迟时间可以诱导系统从单稳态向双稳态转化, 发生相变; 在基因选择过程中, 延迟时间有利于从基因群体中选择出某一单倍体基因. 数值模拟结果与理论预测基本符合.     

An all-optical time-delay relay based on a bacteriorhodopsin film

Using a special property of dynamic complementary-suppression-modulated transmission （DCSMT） in the bacteriorhodopsin （bR） film, we have demonstrated an all-optical time-delay relay. To extend our work, the relationship between the delay time of the all-optical time-delay relay and parameters of a bR film is numerically studied. We show how the delay time changes with the product of concentration and thickness （PCT） of a bR film. Furthermore, the shortest and longest delay times are given for the relay of ＇switch off. The saturable delay time and maximum delaytime of ＇switch on＇ are also given. How the wavelengths （632.8, 568, 533 and 412 nm） and intensities of the illuminating light influence the delay time is also discussed. The simulation results are useful for optimizing the design of all-optical time-delay relays.     

Synchronization transitions in coupled time-delay electronic circuits with a threshold nonlinearity

Experimental observations of typical kinds of synchronization transitions are reported in unidirectionally coupled time-delay electronic circuits with a threshold nonlinearity and two time delays, namely feedback delay τ(1) and coupling delay τ(2). We have observed transitions from anticipatory to lag via complete synchronization and their inverse counterparts with excitatory and inhibitory couplings, respectively, as a function of the coupling delay τ(2). The anticipating and lag times depend on the difference between the feedback and the coupling delays. A single stability condition for all the different types of synchronization is found to be valid as the stability condition is independent of both the delays. Further, the existence of different kinds of synchronizations observed experimentally is corroborated by numerical simulations and from the changes in the Lyapunov exponents of the coupled time-delay systems.     

Conditions for common-noise-induced synchronization in time-delay systems

We studied synchronization induced by a common external noise in scalar time-delay systems. We have found a set of sufficient conditions for the synchronization. This set of conditions shows that the synchronization occurs in a wide class of time-delay systems. Numerical evidence for the analytically obtained conditions is also presented.     

Delay time modulation induced oscillating synchronization and intermittent anticipatory/lag and complete synchronizations in time-delay nonlinear dynamical systems

Existence of a new type of oscillating synchronization that oscillates between three different types of synchronizations (anticipatory, complete, and lag synchronizations) is identified in unidirectionally coupled nonlinear time-delay systems having two different time-delays, that is feedback delay with a periodic delay time modulation and a constant coupling delay. Intermittent anticipatory, intermittent lag, and complete synchronizations are shown to exist in the same system with identical delay time modulations in both the delays. The transition from anticipatory to complete synchronization and from complete to lag synchronization as a function of coupling delay with suitable stability condition is discussed. The intermittent anticipatory and lag synchronizations are characterized by the minimum of the similarity functions and the intermittent behavior is characterized by a universal asymptotic -32 power law distribution. It is also shown that the delay time carved out of the trajectories of the time-delay system with periodic delay time modulation cannot be estimated using conventional methods, thereby reducing the possibility of decoding the message by phase space reconstruction.     

具有时滞状态反馈的随机Van der Pol系统的动力学研究

研究了时滞及时滞反馈控制参数对Van der Pol系统极限环幅值的影响. 运用自适应的平均场近似方法给出了系统的线性化近似及系统参数Lyapunov稳定性的边界条件, 同时给出了Van der Pol系统的关联时间和功率谱密度的数值模拟结果. 通过与平均场近似下的解析结果比较后发现, 数值模拟结果和理论结果符合.进一步讨论了时滞反馈控制参数、噪声强度以及时滞对关联时间和功率谱密度的影响. 关键词： 平均场近似 关联时间 Lyapunov稳定性     

OPTIMAL CONTROL METHOD WITH TIME DELAY IN CONTROL

Optimal control method for active vibration control of linear time-delay systems is investigated in this paper. In terms of two cases that time delay is integer and non-integer times of sampling period, motion equation with time delay is transformed as standard discrete forms which contain no time delay by using zero order holder respectively. Discrete quadratic function is used as objective function in design of controller to guarantee good control efficiency on sampling points. In every step of computation of the deduced controller, it contains not only current step of state feedback but also linear combination of some former steps of control. Because the controller is deduced directly from time-delay differential equation, system stability can be guaranteed easily, thus this method is generally applicable to ordinary control systems. The performance of the control method proposed and system stability when using this method are all demonstrated by numerical simulation results. Simulation results demonstrate that the presented method is a viable and attractive control strategy for applications to active vibration control. Instability in responses occurs possibly if the systems with time delay are controlled using controller designed in case of no time delay.     

阿秒和频相位共轭极化拍频的不对称色锁二阶相干控制

研究了级联三能级系统中孪生色锁随机光场的相位共轭阿秒和频极化拍频(ASPB)不对称新效应。从理论上分析了自关联单光子简并四波混频(DFWM)和双光子非简并四波混频(NDFWM)信号辐射场与物质间不对等效应、混合型太赫兹失谐振荡特性,及双光子非简并共振四波混频信号的延时不对称性;同时也分析了由干涉计两臂不平衡色散效应引起的阿秒和频极化拍频信号的延时不对称性,即阿秒和频极化拍频信号的最大值相对于零延时有一个小偏移,结果表明该不对称性并这不影响阿秒和频极化拍频零差探测两偶极禁戒跃迁能级分裂的总体精度。阿秒和频极化拍频作为一种消除多普勒增宽的超快调制过程,从理论上说它可以扩展到任何两偶极禁戒跃迁能级系统。     

Anticipation in the synchronization of chaotic semiconductor lasers with optical feedback

The synchronization of chaotic semiconductor lasers with optical feedback is studied numerically in a one-way coupling configuration, in which a small amount of the intensity of one laser (master laser) is injected coherently into the other (slave laser). A regime of anticipated synchronization is found, in which the intensity of the slave laser is synchronized to the future chaotic intensity of the master laser. Anticipation is robust to small noise and parameter mismatches, but in this case the synchronization is not complete. It is also shown that anticipated synchronization occurs in coupled time-delay systems, when the coupling has a delay that is less than the delay of the systems.     

Transition from phase to generalized synchronization in time-delay systems

The notion of phase synchronization in time-delay systems, exhibiting highly non-phase-coherent attractors, has not been realized yet even though it has been well studied in chaotic dynamical systems without delay. We report the identification of phase synchronization in coupled nonidentical piecewise linear and in coupled Mackey-Glass time-delay systems with highly non-phase-coherent regimes. We show that there is a transition from nonsynchronized behavior to phase and then to generalized synchronization as a function of coupling strength. We have introduced a transformation to capture the phase of the non-phase-coherent attractors, which works equally well for both the time-delay systems. The instantaneous phases of the above coupled systems calculated from the transformed attractors satisfy both the phase and mean frequency locking conditions. These transitions are also characterized in terms of recurrence-based indices, namely generalized autocorrelation function P(t), correlation of probability of recurrence, joint probability of recurrence, and similarity of probability of recurrence. We have quantified the different synchronization regimes in terms of these indices. The existence of phase synchronization is also characterized by typical transitions in the Lyapunov exponents of the coupled time-delay systems.     

The effect of distributed time-delays on the synchronization of neuronal networks

Here we investigate the synchronization of networks of FitzHugh-Nagumo neurons coupled in scale-free, small-world and random topologies, in the presence of distributed time delays in the coupling of neurons. We explore how the synchronization transition is affected when the time delays in the interactions between pairs of interacting neurons are non-uniform. We find that the presence of distributed time-delays does not change the behavior of the synchronization transition significantly, vis-a-vis networks with constant time-delay, where the value of the constant time-delay is the mean of the distributed delays. We also notice that a normal distribution of delays gives rise to a transition at marginally lower coupling strengths, vis-a-vis uniformly distributed delays. These trends hold across classes of networks and for varying standard deviations of the delay distribution, indicating the generality of these results. So we conclude that distributed delays, which may be typically expected in real-world situations, do not have a notable effect on synchronization. This allows results obtained with constant delays to remain relevant even in the case of randomly distributed delays.     

混沌系统的辅助参考反馈控制

研究了保守系统混沌运动的控制问题．在线性反馈控制方法的基础上提出了一种新的控制方法——辅助参考反馈法,给出了控制参数的选择原则,适当调整反馈系数和参考项即可以得到不同的周期轨道．数值研究证明了该方法能够有效地控制耗散混沌系统和保守系统,同时周期窗口在弱噪声干扰下具有很强的鲁棒性． 关键词：     

Kalman filters for fractional discrete-time stochastic systems along with time-delay in the observation signal

This paper investigates fractional Kalman filters when time-delay is entered in the observation signal in the discrete-time stochastic fractional order state-space representation. After investigating the common fractional Kalman filter, we try to derive a fractional Kalman filter for time-delay fractional systems. A detailed derivation is given. Fractional Kalman filters will be used to estimate recursively the states of fractional order state-space systems based on minimizing the cost function when there is a constant time delay (d) in the observation signal. The problem will be solved by converting the filtering problem to a usual d-step prediction problem for delay-free fractional systems.