一种新的时间序列确定性辨识方法

提出一种新的基于辛几何谱的时间序列确定性检测方法，通过计算原始时间序列及其替代数据的辛几何谱，利用非参数Mann-Whitney 秩和检验方法，可有效地辨别确定性混沌过程和随机过程.通过对常见的随机过程，Lorenz，Rssler，Mackey-Glass，高维耦合方程的仿真检验，说明了方法的有效性. 并通过用Santa Fe测试集中两个序列检验了其对实际时间序列的适用性，最后研究不同数据长度和不同强度噪声对该方法性能的影响说明了其鲁棒性.     

Quantum computer inverting time arrow for macroscopic systems

Since Boltzmann developed the statistical theory for macroscopic thermodynamics the question has relentlessly been put forward of how time-reversibility at microscopic level is compatible with macroscopic irreversibility. Here we show that a quantum computer can efficiently simulate a macroscopic thermodynamic process with chaotic microscopic dynamics and invert the time arrow even in presence of quantum errors. In contrast, small errors in classical computer simulation of this dynamics grow exponentially with time and rapidly destroy time-reversibility. Received 31 October 2001     

Detecting positive feedback in multivariate time series: The case of metal prices and US inflation

The objective of this paper is to examine causality and feedback relationships between primary commodity prices and US inflation. To this end, the bivariate noisy Mackey–Glass process recently developed by Kyrtsou and Labys [Evidence for chaotic dependence between US inflation and commodity prices, J. Macroecon. 28(1) (2006) 256–266] has been applied to assess this relationship. Results obtained support evidence in favour of causality, which can help to identify the influences of speculative price behaviour on inflation.     

采用优化极限学习机的多变量混沌时间序列预测

基于优化极限学习机理论, 提出一种多变量混沌时间序列预测方法. 该方法利用复合混沌和混沌变尺度算法对极限学习机的模型参数进行搜索和优化, 以提高极限学习机的泛化性能; 然后利用优化后的极限学习机对Rossler耦合系统的多变量混沌时序进行一步和多步预测, 并且与同类算法进行了比较, 结果表明了该方法的有效性, 且算法具有较强的抗噪能力; 最后讨论了预测结果和隐层神经元数目的关系.     

离散时间序列的网络模体分析

时间序列可以被转换成网络的形式,复杂网络理论也因此可以用于刻画时间序列的时域和相空间特性.本文针对可视图算法和相空间重构算法这两种时间序列的转换算法,研究了它们的伴生网络在倍周期分岔和混沌等各种类型时间序列的模体分布特征,分析了这两种算法各自的优点.     

基于时间透镜原理实现微波信号时间反演

时间反演电磁学是一门新兴学科. 高效的电磁时间反演信号获取方式是时间反演技术获得应用的关键. 本文研究了一种基于时域成像原理获得时间反演微波信号的方法. 首先根据时间透镜原理, 推导出了实现波形时间反演的条件, 并对波形反演的过程进行了数值仿真. 然后设计了两种满足反演条件的啁啾电磁带隙结构来构造色散信道, 并通过实验得到了一个时隙长度为1.5 ns的时间反演信号. 由于啁啾电磁带隙结构与理想色散信道的差异, 实验结果中存在波形失真. 文章最后对造成失真的原因进行了分析.     

Complex network approach for recurrence analysis of time series

We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix (calculated from time series) with the adjacency matrix of a complex network and apply measures for the characterisation of complex networks to this recurrence matrix. By using the logistic map, we illustrate the potential of these complex network measures for the detection of dynamical transitions. Finally, we apply the proposed approach to a marine palaeo-climate record and identify the subtle changes to the climate regime.     

Heterogeneous recurrence representation and quantification of dynamic transitions in continuous nonlinear processes

Many real-world systems are evolving over time and exhibit dynamical behaviors. In order to cope with system complexity, sensing devices are commonly deployed to monitor system dynamics. Online sensing brings the proliferation of big data that are nonlinear and nonstationary. Although there is rich information on nonlinear dynamics, significant challenges remain in realizing the full potential of sensing data for system control. This paper presents a new approach of heterogeneous recurrence analysis for online monitoring and anomaly detection in nonlinear dynamic processes. A partition scheme, named as Q-tree indexing, is firstly introduced to delineate local recurrence regions in the multi-dimensional continuous state space. Further, we design a new fractal representation of state transitions among recurrence regions, and then develop new measures to quantify heterogeneous recurrence patterns. Finally, we develop a multivariate detection method for on-line monitoring and predictive control of process recurrences. Case studies show that the proposed approach not only captures heterogeneous recurrence patterns in the transformed space, but also provides effective online control charts to monitor and detect dynamical transitions in the underlying nonlinear processes.     

基于直接延迟反馈的混沌反控制

在混沌有益时，有目的地产生混沌已经成为混沌学研究的热点问题，本文提出直接延迟反馈实现混沌的反控制，在非混沌系统中产生了混沌.该方法与间接延迟反馈控制方法相比，控制更加简单，更易于实现.该方法与Pyragas提出的延迟反馈混沌控制方法的控制器结构相同，因此，这种直接延迟反馈控制方法可以在需要混沌时产生混沌，不需要混沌时控制混沌，实现混沌控制和反控制的统一，为设计者提供最大的灵活性.针对参数处于非混沌区的Chen系统和Lorenz系统的仿真结果表明了该混沌反控制方法的有效性. 关键词： 混沌 反控制 直接延迟反馈     

一类关联混沌系统的分时切换混沌同步

提出关联混沌系统分时切换混沌同步的思想.利用线性反馈控制方法实现一类关联混沌系统中各个子系统与其复制系统间的分时切换混沌同步.根据时变系统的稳定性理论，得到了使各子系统都能实现混沌同步的反馈控制增益的取值范围.数值仿真实验证明了理论分析的正确性和可行性.     

一类关联混沌系统的分时切换混沌同步

提出关联混沌系统分时切换混沌同步的思想.利用线性反馈控制方法实现一类关联混沌系统中各个子系统与其复制系统间的分时切换混沌同步.根据时变系统的稳定性理论,得到了使各子系统都能实现混沌同步的反馈控制增益的取值范围.数值仿真实验证明了理论分析的正确性和可行性. 关键词： 分时切换混沌同步 线性反馈 关联混沌系统     

Inverse chaos synchronization between bidirectionally coupled variable multiple time delay systems

We make first report on inverse chaos synchronization between bidirectionally non-linearly and linearly coupled variable multiple time delay laser systems governed by the Ikeda model. The results are of certain importance in secure chaos-based communication systems.     

基于最大Lyapunov指数不变性的混沌时间序列噪声水平估计

提出了一种基于最大Lyapunov指数不变性的计算混沌时间序列噪声水平的新方法. 首先分析了噪声对相空间中两点距离的影响, 然后基于最大Lyapunov指数在不同维数的嵌入相空间不变的性质, 建立了估计噪声水平的方法. 仿真计算结果表明, 当噪声水平小于10% 时, 估计值与真实值符合良好. 该方法对噪声分布类型不敏感, 是一种有效的混沌时间序列噪声估计方法.     

Mean first passage time of active Brownian particle in one dimension

We investigate the mean first passage time of an active Brownian particle in one dimension using numerical simulations. The activity in one dimension is modelled as a two state model; the particle moves with a constant propulsion strength but its orientation switches from one state to other as in a random telegraphic process. We study the influence of a finite resetting rate r on the mean first passage time to a fixed target of a single free active Brownian particle and map this result using an effective diffusion process. As in the case of a passive Brownian particle, we can find an optimal resetting rate r* for an active Brownian particle for which the target is found with the minimum average time. In the case of the presence of an external potential, we find good agreement between the theory and numerical simulations using an effective potential approach.     

Dynamical hysteresis and spatial synchronization in coupled non-identical chaotic oscillators

We identify a novel phenomenon in distinct (namely non-identical) coupled chaotic systems, which we term dynamical hysteresis. This behavior, which appears to be universal, is defined in terms of the system dynamics (quantified for example through the Lyapunov exponents), and arises from the presence of at least two coexisting stable attractors over a finite range of coupling, with a change of stability outside this range. Further characterization via mutual synchronization indices reveals that one attractor corresponds to spatially synchronized oscillators, while the other corresponds to desynchronized oscillators. Dynamical hysteresis may thus help to understand critical aspects of the dynamical behavior of complex biological systems, e.g. seizures in the epileptic brain can be viewed as transitions between different dynamical phases caused by time dependence in the brain’s internal coupling.     

Energy relaxation time between macroscopic quantum levels in a superconducting persistent-current qubit

We measured the intrawell energy relaxation time tau(d) approximately 24 micros between macroscopic quantum levels in the double well potential of a Nb persistent-current qubit. Interwell population transitions were generated by irradiating the qubit with microwaves. Zero population in the initial well was then observed due to a multilevel decay process in which the initial population relaxed to lower energy levels during the driven transitions. The decoherence time, estimated from tau(d) within the spin-boson model, is about 20 micros for this configuration with a Nb superconducting qubit.     

Robust pre-specified time synchronization of chaotic systems by employing time-varying switching surfaces in the sliding mode control scheme

In the conventional chaos synchronization methods, the time at which two chaotic systems are synchronized, is usually unknown and depends on initial conditions. In this work based on Lyapunov stability theory a sliding mode controller with time-varying switching surfaces is proposed to achieve chaos synchronization at a pre-specified time for the first time. The proposed controller is able to synchronize chaotic systems precisely at any time when we want. Moreover, by choosing the time-varying switching surfaces in a way that the reaching phase is eliminated, the synchronization becomes robust to uncertainties and exogenous disturbances. Simulation results are presented to show the effectiveness of the proposed method of stabilizing and synchronizing chaotic systems with complete robustness to uncertainty and disturbances exactly at a pre-specified time.     

Effects of time delays in a mathematical bone model

In this paper we propose a mathematical model of bone remodeling with time delays of both osteoclast-derived paracrine signaling of tumor and tumor-derived paracrine signaling of osteoclast. The effects of time delays on the growth of tumor cells and bone system are studied in multiple myeloma-induced bone disease. In the case of small osteoclast-derived paracrine signaling, it is found that the growth of tumor cells slows down, the oscillation period of the ratio of osteoclasts to osteoblasts is extended with increasing time delay, and there is a competition between the delay and osteoclast-derived paracrine signaling. In the case of large tumor-derived paracrine signaling, the tumor-derived paracrine signaling can induce a more significant decline in tumor growth for long time delay, and thus slowing down the progression of bone disease. There is an optimal coupling between the tumor-derived paracrine signaling of osteoclasts and time delay during the progressions of bone diseases, which suppresses the tumor growth and the regression of bone disease.     

时标正弦动力学方程稳定性与分岔分析

本文研究时标上正弦动力学方程的平衡点稳定性和分岔现象. 研究表明随时标参数的变化,正弦动力学方程展现出完全不同的解, 会产生n倍周期分岔和平衡点分裂等特有现象.同时,不增加系统参数, 仅改变时标的复杂性就能扩展动力学方程处于混沌状态的参数空间, 这为时标上动力学方程在混沌加密和雷达波形设计等领域的应用提供了潜在的优势.     

Advection and dispersion in time and space

Previous work showed how moving particles that rest along their trajectory lead to time-nonlocal advection–dispersion equations. If the waiting times have infinite mean, the model equation contains a fractional time derivative of order between 0 and 1. In this article, we develop a new advection–dispersion equation with an additional fractional time derivative of order between 1 and 2. Solutions to the equation are obtained by subordination. The form of the time derivative is related to the probability distribution of particle waiting times and the subordinator is given as the first passage time density of the waiting time process which is computed explicitly.