Prediction and analysis of chaotic time series on the basis of support vector

Based on discussion on the theories of support vector machines （SVM）, an one-step prediction model for time series prediction is presented, wherein the chaos theory is incorporated. Chaotic character of the time series is taken into account in the prediction procedure; parameters of reconstruction-detay and embedding-dimension for phase-space reconstruction are calculated in light of mutual-information and false-nearest-neighbor method, respectively. Precision and functionality have been demonstrated by the experimental results on the basis of the prediction of Lorenz chaotic time series.     

A Novel Integrated Measure for Energy Market Efficiency

This paper formulates a novel integrated measure for energy market efficiency, by investigating different aspects of the market performance. Different from most existing models focusing on one certain aspect, the novel measure especially takes into consideration the self-similarity(or system memo ability or long-term persistence) via fractality, the attractor properties in phase-space via chaos,and disorder state of data dynamics via entropy. In the proposed method, the most popular data analysis techniques of multi-fractal detrended fluctuation analysis, correlation dimension, and sample entropy are respectively conducted on the market returns to capture the corresponding features, and the entropy weight method is then used to generate the final integrated index. For illustration and verification, the proposed measure is applied to three typical energy markets analyses. The empirical results find that natural gas market and crude oil market are much more efficient than carbon market.     

Dynamic price model based on transmission delay — Petroleum price fluctuation in China

Petroleum is a kind of fundamental energy resource. Its price fluctuation transmits from upper-stream industry to the lower-stream industry as the production factors price changes. And this leads to the price changes of final consumption. Meantime, due to the cycle of industrial chain, the price changes of lower-stream industry also affect the upper-stream industry in return. This price transmission path is quite complicated. Firstly, it includes both direct and indirect paths; secondly, the transmission process is accompanied with time delay. The traditional input-output price model based on cost-push theory can efficiently solve the first problem when estimating the impact of price fluctuation on the whole price system. However, it neither reflects the dynamic characteristics of price transmission with time nor solves the second problem. To solve this problem, this paper uses the directed weighted network to describe the price transmission among industrial sectors by taking the time-dimension into account, and dynamic price transmission network model is constructed. This model not only describes transmission time delay more accurately, but also calculates the price fluctuation dynamically. On this basis, by utilizing the 2007 Chinese input-output table, this paper conducts empirical analysis on the impact of petroleum price fluctuation on other sectors. The empirical results indicate that the price fluctuation transmission mainly depends on two factors, the orice reaction period Tk and the consumption relationship with petroleum aik. 1） If t 〈 Tk, then the price change of sector k at period t △pkt = 0, the petroleum price fluctuation has not transmitted to the sector k, so the price of sector k remains unchanged. 2） If t 〉 Tk, then Apt 〉 0, and the greater aik, the higher price change rate. 3） If t →∞, it is the same with that in traditional input-output price model. So it can be clearly seen that dynamic price transmission network model is more general than the traditional model, and the traditional model is just an asymptotical special case when time approaches to infinity. Keywords Directed weighted network, input-output price model, petroleum price, transmission time delay.     

基于小波与混沌集成的中国股票市场预测

应用小波变换和混沌理论提出了一种中国股票市场建模及其预测的小波与混沌集成的方法．首先应用小波分解理论对上证综指和深证成指日收益率序列进行分解，分别得到低频部分和高频部分，并在此基础上作进一步分析，结果表明中国股市存在混沌特性；然后应用混沌理论分别建立低频部分和高频部分的预测模型，对低频部分和高频部分进行预测；最后应用小波理论对混沌模型预测的结果予以重构，实现对原始收益率序列的预测．与现有方法比较，结果表明该方法具有较高的精度，有极大的应用前景．     

非线性自回归时序模型研究及其预测应用

从函数逼近和系统辨识两个方面推导了非线性自回归时序模型(GNAR模型)的物理结构,通过公式推导及仿真数据研究GNAR模型与确定性实函数、经典时序模型和混沌序列的关系,明确GNAR模型对系统逼近的机理.以Lorenz系统输出的混沌序列和现代经典时序-太阳黑子序列为算例进行数据实验,证明了GNAR模型在建模和预测方面的优越性.     

Global stability of an age-structured sir epidemic model with pulse vaccination strategy

This paper discusses the application of a pulse vaccination strategy to prevent and control some infectious diseases,which is described by age-structured SIR model in which susceptible and recovered individuals are structured by chronological age,while infected individuals are structured by infection age(duration since infection).The time dependent disease-free equilibrium is determined, for which an explicit expression exists.The analytical results show that there exists a globally stable infect ion-free situation if the impulsive period T and proportion p satisfy Ro(p,T) < 1.Optimal problem is discussed:Pulse vaccination strategy with minimal costs at given Ro(p,T) < 1.     

应用小波理论进行股市预测

应用小波理论提出一种股票市场建模及其预测的方法,以上证综指为例进行了实证研究,并从吸引子结构的观点进一步分析了预测精度提高的原因。采用此方法进行股市预测,首先要应用小波理论对股指收益率序列进行分解,得到低频和高频部分;然后在此基础上作进一步分析,以确定各部分存在混沌特性;再应用混沌理论分别建立低频和高频部分的预测模型,对低频和高频部分进行预测;最后应用小波理论对混沌模型预测的结果予以重构,实现对原始收益率序列的预测。研究结果表明,该方法具有较高的精度,并具有极大的应用前景。     

双混沌神经网络及其在优化问题中的应用

分析了三种现有的混沌神经网络模型的优化性能,针对目前混沌神经网络收敛率不高和搜索时间较长的问题提出了一种双混沌神经网络。它不同于以往的混沌神经网络改进方法,不是延长退火时间或改变混沌程度来提高网络性能,而是通过混沌迭代搜索使混沌神经网络在有限步内找到全局最优解的初值来提高收敛率与收敛速度。这种方法能使混沌神经网络在应用中具有更好的全局优化能力,并且可以缩短混沌神经网络的搜索时间,对旅行商问题求解的仿真对比和函数优化问题的仿真,说明了新方法比现有方法具有更好的收敛率和更短的搜索时间。     

Rossler系统与统一混沌系统的异结构同步

针对异结构混沌系统的同步提出了两种不同的同步方案,研究了两个不同结构的混沌系统:Rossler系统与统一混沌系统的同步。系统参数已知时采用主动控制方法,通过设计适当的主动控制器,实现了响应系统与驱动系统的渐近同步;系统参数不确定或未知时采用自适应控制方法,基于李亚普诺夫稳定性理论,得出了两异结构混沌系统同步的充分条件,设计了相应的控制器和参数自适应律,使得响应系统的状态变量渐近跟踪驱动系统的状态变量,且两个系统的参数估计值渐近收敛于其真值,仿真结果证明了两种方案的有效性。     

SDN子网进化博弈研究

基于replicator dynamics(RD)模型的构建思想,提出了SDN(supply and demand network with mul-tifunction and opening characteristics for enterprise)子网的进化博弈模型,进而构造出了合作博弈策略混沌演化的数学模型。在RD模型的局部稳定点分析基础上,利用该数学模型生成了合作博弈的混沌演化模拟图,通过博弈的混沌演化模拟,从混沌演化的角度深入探讨了ESS的动态形成过程,佐证了SDN子网的混沌演化规律,验证了不同博弈阶段的子网结构也同样经历混沌的演化过程。这有助于预测SDN及其子网中群体行为的变化趋势,同时对进化博弈理论的动态研究也有一定的参考价值。     

多层混沌神经网络及其在交通量预测中的应用

研究多层混沌神经网络及其在交通量预测中的应用问题。以BP网络和混沌理论为基础,提出了一种在隐层中包含混沌神经元的多层混沌神经网络。XOR问题实验得出:该混沌神经网络能有效地强化网络的非线性和学习效率。鉴于城市交通流具有明显的混沌特性,将该混沌神经网络应用于城市交通流的预测。对广东江门市某路口交通量的预测结果显示出:采用该混沌神经网络,预测误差一般可以控制在10%以下(或左右)。该网络还可以应用于其他混沌系统的预测和控制。     

有限理性行为规则下豪泰林模型的复杂性

构建有限理性行为规则下的豪泰林(Hotelling)模型,分析参与人具有延迟反馈控制行为的豪泰林模型的复杂性.模型求解和数值模拟得出结论:在有限理性情况下,产品价格调整系数、产品位值和偏离成本等参数的取值范围决定了动态系统的稳定性、产量分岔、利润分岔和混沌;产品价格调整系数取值控制在适当范围,豪泰林均衡能够作为稳定的动态均衡实现.否则,即使企业实现了产品差异最大化豪泰林模型的均衡也可能不稳定,经济系统会出现周期变化和混沌现象;如果经济系统进入混沌状态,参与人对价格初值微小的调整都会引起价格发生巨大的波动;延迟反馈控制可以使处于混沌状态的系统转向均衡状态;同时论证了企业产品横向差异化可增加系统的稳定性.     

一类厂商业务量决策模型的改进及复杂性研究

参与人出于财务、生产能力、谨慎等方面的考虑,通常会对其业务量作一定限制,以避免其业务量过高或过低.考虑到这一情况,对有限理性的Bischi模型进行改进,对参与人每期的业务量加下限或(和)上限的限制,使之更符合实际.以添加下限为例,对改进后模型的动态性进行分析并与原模型进行对比.从分析中可以看到,下限在一定范围内取值时模型仍出现复杂的混沌行为,但与原模型有显著差别.在下限的取值达到一定程度时,模型的混沌现象会消失,出现稳定的周期行为.这个结果说明参与人可通过给状态变量加下限的方法来预防或抑制某些经济系统中的混沌.     

国际碳排放权市场分形与混沌行为特征分析与检验——以欧盟碳排放交易体系为例

本文利用Bluenext和ECX的经验数据,对欧盟碳排放权市场(EU-ETS)的价格行为特征进行了分析.研究表明:1)对EU-ETS市场收益率序列基本统计特征检验显示:碳收益率序列不服从正态分布,具有明显的有偏、尖峰、肥尾的非正态性和非线性的统计分布特征;2)对市场分形性的研究表明:该市场具有显著的统计自相似性,阶段性的、而非全过程的长期记忆性特征;3)对市场混沌性的研究表明:从关联维数看,EU-ETS并不存在低维混沌性,但结合最大Lyapunov指数检验及邻近返回检验证明欧盟碳排放权市场存在非收敛饱和混沌性.由此得出结论:欧盟碳排放权市场是一个具有分形与混沌特征的非线性动力系统,它不符合有效市场假说,因此不能用线性范式来研究市场价格行为、交易机制及政策制定.     

一种在线实时快速地判定交通流混沌的组合算法

交通控制的实时性要求高，需要在线实时快速地判定交通流混沌，才可能实现交通流的混沌控制。计算时间序列的最大Lyapunov指数是判定混沌的主要方法。本文提出一种在线实时快速地判定交通流混沌的组合算法。该算法先用关联积分法（C—C方法）确定重构相空间的两个重要参数——嵌入维m和延迟时间τ，再用小数据量方法计算时间序列的最大Lyapunov指数。为检验算法的有效性，首先将算法用于几个最大Lyapunov指数已知的经典混沌系统，比较计算结果；同时对皮埃莱（Bierley）跟驰模型产生的理论交通流时间序列做了仿真试验，计算了其最大Lyapunov指数。实验结果表明这种算法可以用于数据少的交通流时间序列，并且抗噪性好。     

随机数发生器的噪声模型与快速仿真

在随机数发生器设计过程中,采用Spice虽然能对模拟电路进行比较精确的仿真,但耗时太久,同时它的数据处理工作也非常繁琐,不易进行统计分析。为了解决这一问题,在分析了一个分段线性映射的、决定论混沌的随机数发生器的基础上,根据它的混沌公式提出了基本的仿真原理。为了提高仿真的准确性,针对CMOS电路中主要的噪声,即MOS管的热噪声与闪烁噪声,建立了二种噪声仿真模型。在分析电路行为的同时,逐步提出了采用MATLAB/Simulink的随机数发生器单元电路模型,然后建立了随机数发生器系统模型,实现了快速计算过程。最后给出了系统模型的仿真测试结果。     

Solutions for singular p-Laplacian equation in R n

In this paper, the authors study the existence and non-existence of positive solutions for singular p-Laplacian equation −∆ _p u = f(x)u ^−α + λg(x)u ^β in R ^N ; where N ≥ 3, 1 < p < N, λ > 0, 0 < α < 1, max(p, 2) < β + 1 < p* = \fracN_pN - p \frac{{{N_p}}}{{N - p}} . We prove that there exists a critical value ¤ such that the problem has at least two solutions if 0 < λ < Λ; at least one solution if λ = Λ; and no solutions if λ > Λ.     

COMBINING SINGULAR SPECTRUM ANALYSIS AND PAR（p） STRUCTURES TO MODEL WIND SPEED TIME SERIES

Singular spectrum analysis （SSA） is a technique that decomposes a time series into a set of components, such as, trend, harmonics, and residuals. Leaving out the residual components and adding up the others, the time series can be smoothed. This procedure has been used to model Brazilian electricity consumption and flow series. The PAR（p）, periodic autoregressive models, has been broadly used in modelling energy series in Brazil. This paper presents an approach of this decomposition method, by fitting the PAR（p）, considering its multivariate version known as multivariate SSA （MSSA）. The method was applied to a vector of two wind speed series recorded at two locations in the Brazilian Northeast region. The obtained results, when compared to the univariate decomposition of each series, were far superior, showing that the spatial correlation between the two series were considered by MSSA decomposition stage.     

Optimization of HMM Parameters Based on Chaos and Genetic Algorithm for Hand Gesture Recognition

In order to prevent standard genetic algorithm (SGA) from being premature, chaos is introduced into GA, thus forming chaotic anneal genetic algorithm (CAGA). Chaos' ergodicity is used to initialize the population, and chaotic anneal mutation operator is used as the substitute for the mutation operator in SGA. CAGA is a unified framework of the existing chaotic mutation methods. To validate the proposed algorithm, three algorithms, i. e. Baum-Welch, SGA and CAGA, are compared on training hidden Markov model (HMM) to recognize the hand gestures. Experiments on twenty-six alphabetical gestures show the CAGA's validity.     

Extended ambiguity function for bistatic MIMO radar

This paper derives the extended ambiguity function for a bistatic multiple-input multiple-output (MIMO) radar system,which includes the whole radar system parameters:geometric sensor configuration,waveforms,range,range rate,target scattering and noise characteristics.Recent research indicates the potential parameter estimate performance of bistatic MIMO radars.And this ambiguity function can be used to analyze the parameter estimate performance for the relationship with the Cramer-Rao bounds of the estimated parameters.Finally,some examples are given to demonstrate the good parameter estimate performance of the bistatic MIMO radar,using the quasi-orthogonal waveforms based on Lorenz chaotic systems.