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1.
根据数值计算的结果提出了模态耦合的条件,两个方程在高频模态上是耦合的,而在低频模态上是不耦合的.利用了无穷维动力系统理论,证明了两个高频模态耦合的Ginzburg-Landau方程在函数空间中存在吸引域,因而存在连通的、有限维的紧的整体吸引子.驱动方程存在时空混沌.将方程组联系一个截断形式,得到的修正方程组将保持原方程组的动力学行为.高频模态耦合的两个方程在一定的条件下具有挤压性质,证明了可达到完全的时空混沌同步化.在数学上定性解释了无穷维动力系统的同步化现象.研究方法不同于有限维动力系统中通常使用的Liapunov函数方法与近似线性方法.  相似文献   

2.
混沌时间序列在自然界以及人们的生产生活中很常见,混沌序列看似杂乱无章但相较于纯随机序列其中蕴含着一些非线性的运动特征,提出一种基于多尺度自适应阶ARMA的混沌时间序列多步预测方法.首先利用自适应噪声的完备经验模态分解(CEEMDAN)对原始混沌序列进行分解,获得不同尺度的固有模态分量(IMF)和残余分量.然后采用经粒子群算法(PSO)进行阶数寻优的自回归移动平均模型(ARMA)对每一个IMF分量进行拟合预测.最后将预测得到的每一个分量相加得到原始混沌序列的预测值.基于Mackay-Glass混沌序列和太阳黑子数混沌序列进行实验分析,实验表明:与ARMA、PSO-ARMA以及CEEMDAN-ARMA方法相比,方法的预测效果有较好的提高,其平均绝对误差(MAE)、均方根误差(RMSE)以及平均绝对百分比误差(MAPE)都有降低.  相似文献   

3.
低噪声水平混沌时序的预测技术及其应用研究   总被引:3,自引:0,他引:3  
研究含有噪声的混沌时序的除噪及其重构技术,基于除噪混沌数据的预测技术及其应用.应用混沌时序的奇异值分解技术对混沌时序的噪声进行了剥离,将混沌时序的相空间分解成为值域空间和虚拟的噪声空间,在值域空间内重构了原混沌时序,并在此基础上,确立了非线性模型的阶,利用所提出的非线性模型对时序进行了预测研究工作,研究结果表明,该非线性模型具有很强的函数逼近能力,所采用的混沌预测方法对相应的实际问题有着一定的指导意义.  相似文献   

4.
该文对连续动力系统研究了Devaney意义下的混沌的不变性质.证明了:(1)半流是混沌的(resP,ω混沌的)当且仅当它的逆极限是混沌的(resp,ω混沌的);(2)自映射是混沌的(resp.ω混沌的)当且仅当它的扭扩半流是混沌的(resp.ω混沌的);(3)自映射逆极限的扭扩流拓扑共轭于其扭扩半流的逆极限.从(2)和(3)可知,结论(1)是对自映射的推广.  相似文献   

5.
针对ECG信号的非线性和非平稳性,利用不同经验模态分解的小波软阈值方法对其进行降噪处理.根据希尔伯特-黄(Hilbert-Huang)变换提出的一系列的EMD算法,有EMD、EEMD、CEEMD等.首先,将含高斯白噪声的ECG信号分别进行EMD、EEMD、CEEMD分解,所得到的固有模态函数(IMF)分量是从高频到低频排列的,分别舍去前几层含噪IMF'进行重构去噪.由于舍去的IMF分量中含有少部分信号的细节信息,然后利用小波软阈值对前几层含噪IMF提取细节信息得到新的分量,再将剩余分量和新的分量重构去噪后的ECG信号.利用去噪信号图和不同性能指标验证了不同方法的有效性,得出了基于CEEMD的小波软阈值ECG降噪效果最佳.最后,用上述方法对MIT-BIH心电噪声库信号进行去噪处理,其结果与仿真实验相吻合.  相似文献   

6.
孙联荣  戴再平 《数学通报》2007,46(12):24-26
按答案的结构不同,我们可以把数学开放题分成四类:(一)有限穷举型;(二)有限混沌型;(三)无限离散型;(四)无限连续型.下面以“单位分数”问题为例,谈谈“有限混沌型”开放题的探究.  相似文献   

7.
针对传感器水声信号存在随机噪声的问题,提出了一种正余弦算法(SCA)和粒子群算法(PSO)相结合优化变分模态分解(VMD)参数k和α,将含噪信号通过VMD分解为k个固有模态函数,选取相关系数高的模态分量进行小波阈值(WT)去噪后重构信号分量,得到目标信号的算法,记为SCA-PSO-VMD-WT算法.通过将本算法与VMD-WT,PSO-VMD-WT,SCA-VMD-WT算法相比,并从信噪比、均方误差2个评估指标发现本算法的去噪效果最好.  相似文献   

8.
区域分解界面预条件子构造的一般框架   总被引:1,自引:1,他引:0  
胡齐芽  梁国平 《计算数学》1999,21(1):117-128
1.引言考虑模型问题:其中ΩR2是多边形区域,常数n≥0.将Ω作非重叠区域分解:Ω=假定:(i)当i≠j时,(ii)当Ωi与Ωj相邻时,是Ωi和Ωj的一条公共边记称为界面);(iii)每个闪的尺寸为d,即存在常数co和q,使出包含(包含在)一个直径为C()(Cod)的圆(国内).非重叠区域分解方法的实质是,引进两个变量:内部变量。h和界面变量~.先在几上并行未解子问题,将。。消去(即用~表示),得到~的方程(称为界面方程);再求解界面方程,得到~的值;最后将~回代,得到。人的值(即原问题的解).这类区域分解方法是否比重…  相似文献   

9.
小波和EMD的滤波特性在轴承故障诊断中的比较   总被引:1,自引:0,他引:1  
通过仿真实验将小波变换和经验模态分解(EMD)方法分解信号的能力进行了比较,并将这种滤波特性应用于旋转机械的故障诊断中,结合包络谱分析,比较了两者对于滚动轴承内圈故障的诊断效果.仿真及轴承实验结果表明EMD方法在滤波的自适应性、分解结果的准确性以及诊断效果等方面均具有优势,更重要的是它分离出的主要分量物理意义明确,反映了信号的真实内涵.  相似文献   

10.
情感计算是情感语音识别的关键.经验模态分解(EMD)算法是Hilbert-Huang变换(HHT)的核心算法,采用分段幂函数插值算法求情感包络线,能达到更好的情感识别效果.利用软件MATLAB仿真了情感语音信号的经验模态分解(EMD)特性,把情感语音信号进行EMD分解后IMF做频谱变换,便能得到一个情感包络线,根据情感包络线的不同而达到情感识别的目的.  相似文献   

11.
We consider different ways for encryption and decryption of information in communication systems using chaotic signal of a time-delay system as a carrier. A method is proposed for extracting a hidden message in the case when the parameters of the chaotic transmitter are a priori unknown. For different configurations of the transmitter the procedure of information signal extraction from the transmitted signal is demonstrated using numerical data produced by nonlinear mixing of the chaotic signal of the Mackey–Glass system and frequency-modulated harmonic signal.  相似文献   

12.
13.
Digital watermarking is an ever increasing and important discipline, especially in the modern electronically-driven world. Watermarking aims to embed a piece of information into digital documents which their owner can use to prove that the document is theirs, at a later stage. In this paper, performance analysis of watermarking schemes is performed on white noise sequences and chaotic sequences for the purpose of watermark generation. Pseudorandom sequences are compared with chaotic sequences generated from the chaotic skew tent map. In particular, analysis is performed on highpass signals generated from both these watermark generation schemes, along with analysis on lowpass watermarks and white noise watermarks. This analysis focuses on the watermarked images after they have been subjected to common image distortion attacks. It is shown that signals generated from highpass chaotic signals have superior performance than highpass noise signals, in the presence of such attacks. It is also shown that watermarks generated from lowpass chaotic signals have superior performance over the other signal types analysed.  相似文献   

14.
The problem of secure communication via parameter modulation in a chaotic system is considered. Information signals are used to modulate various parameters of a chaotic system. The resulting chaotic signal is later demodulated and the information signals are recovered using an adaptive demodulator. The convergence of the demodulator is established and simulation results validate the theoretical predictions.  相似文献   

15.
With the increasing needs of global communication, the improvement of secure communication is of vital importance. This study proposes a new scheme for establishing secure communication systems. The new scheme separates white Gaussian noises from the chaotic signals with modified Independent Component Analysis (ICA) and then controls each chaotic signal. This scheme is able to deal with white Gaussian noises in the natural world. However, the signals separated by traditional ICA shows opposite phase and unequal amplitude, making chaos control impossible. Our study proposed a modified ICA, which can calculate accurately the phase and amplitude and ensure control of the chaotic systems. The result indicates that our proposed system can successfully separate white Gaussian noise and stabilize all the chaotic signals.  相似文献   

16.
We propose a chaos time-domain reflectometry (CTDR) for locating faults on live wires. This method uses a chaotic output of an improved Colpitts oscillator as probe signal, and detects wire faults by correlating a duplicate with the echo of the probe signal. Benefiting from the anti-jamming of the correlation function of the wideband chaos, fault location on live wires can be achieved. We experimentally demonstrate the detection for live wires in a digital communication system, in which a type of digital signal named high density bipolar of order 3 (HDB3) is transmitted. The effects of the chaotic probe signal on the bit error rate (BER) of the transmitted HDB3 at different rates are analyzed. Meanwhile, the influences of the backward HDB3 reflected by wiring faults on the signal-noise-ratio (SNR) of CTDR measurement are examined experimentally. The results show that fault detection on live wires is achieved when the power of the chaotic probe signal is about from -24.8 dB to -13.5 dB lower than that of the transmitted digital signal. In this case, the BER is kept less than 3E-10, and the SNR of CTDR is higher than 3 dB. Besides, the auto-correlation properties of the improved Colpitts oscillator at different states are investigated experimentally to explore the suitable chaotic states for the CTDR.  相似文献   

17.
We present recent work of harmonic and signal analysis based on the complex Hardy space approach.  相似文献   

18.
From the unicity and orthogonality properties of chaotic sequences, it is demonstrated that a sum of N chaotic signals generated from a fixed class of chaotic systems is unique. Consequently, within a framework of a multi-user transmission, it is shown that synchronizing N chaotic carriers that emit simultaneously on the same frequency band is feasible. In this paper, the carriers are generated from Chua’s circuits and are modulated in amplitude by the information signal. Demodulation is ensured by the minimization of a cost function. Numerical simulations show that this synchronization method is robust in presence of noise and allows the integration of a high number of users.  相似文献   

19.
Josephson junction oscillators can generate chaotic signals with a wide frequency spectrum. An improved scheme of Lyapunov functions is proposed to control chaotic resonators of this type and forces them to converge to an arbitrary selected target signal. A changeable gain coefficient is introduced into the Lyapunov function, and the controllers are designed analytically. The controllers operate automatically when the output series are deviated from the target orbit synchronously. A resistive‐capacitive‐inductive‐shunted Josephson junction in chaotic parameter region is investigated in our studies, and power consumption is estimated from the dimensionless model. It is found that the power consumption of controller is dependent on the amplitude and/or angular frequency of the external target signal to be tracked. For example, larger power costs are observed when the target signal is in larger amplitude and/or angular frequency. The numerical results are consistent with the analytical discussion. © 2014 Wiley Periodicals, Inc. Complexity 21: 370–378, 2015  相似文献   

20.
In this paper, we have examined effects of forcing a periodic Colpitts oscillator with periodic and chaotic signals for different values of coupling factors. The forcing signal is generated in a master bias-tuned Colpitts oscillator having identical structure as that of the slave periodic oscillator. Numerically solving the system equations, it is observed that the slave oscillator goes to chaotic state through a period-doubling route for increasing strengths of the forcing periodic signal. For forcing with chaotic signal, the transition to chaos is observed but the route to chaos is not clearly detectable due to random variations of the forcing signal strength. The chaos produced in the slave Colpitts oscillator for a chaotic forcing is found to be in a phase-synchronized state with the forced chaos for some values of the coupling factor. We also perform a hardware experiment in the radio frequency range with prototype Colpitts oscillator circuits and the experimental observations are in agreement with the numerical simulation results.  相似文献   

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