A singular value decomposition approach to detect chaos innonlinear circuits and dynamic systems

Baglio S.; Fortuna L.

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A singular value decomposition approach to detect chaos innonlinear circuits and dynamic systems

机译：检测非线性电路和动态系统混沌的奇异值分解方法

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In this paper the analogy between Lyapunov exponents and the singular values of the covariance matrix is introduced and two new conjectures are stated. On this basis a new numerical procedure to classify the steady-state behavior of nonlinear dynamic systems from noisy time series data is presented. In order to show the suitability of the proposed approach, several applications to time series data gathered from measurements on experimental circuits are reported

机译：本文介绍了Lyapunov指数与协方差矩阵的奇异值之间的类比，并提出了两个新的猜想。在此基础上，提出了一种新的数值程序，用于从噪声时间序列数据中对非线性动态系统的稳态行为进行分类。为了表明该方法的适用性，报告了对从实验电路测量中收集的时间序列数据的几种应用

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《IEEE Transactions on Circuits and Systems. I, Regular Papers》 |1994年第12期|p.908-912|共5页
作者
Baglio S.; Fortuna L.;
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原文格式 PDF
正文语种 eng
中图分类 TN71;
关键词
Lyapunov methods; chaos; covariance matrices; nonlinear dynamical systems; nonlinear network analysis; singular value decomposition; time series; Lyapunov exponents; chaos; covariance matrix; noisy time series data; nonlinear circuits; nonlinear dynamic systems; sing;

机译：Lyapunov方法;混沌;协方差矩阵;非线性动力系统;非线性网络分析;奇异值分解;时间序列;Lyapunov指数;混沌;协方差矩阵;噪声时间序列数据;非线性电路;非线性动态系统;唱歌;

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1. A singular value decomposition approach to detect chaos in nonlinear circuits and dynamic systems [J] . Baglio S., Fortuna L. IEEE Transactions on Circuits and Systems. 1 . 1994,第12期

机译：检测非线性电路和动态系统中混沌的奇异值分解方法
2. Dynamics of large scale coupled structural/mechanical systems: A singular perturbation/proper orthogonal decomposition approach [J] . Georgiou Ioannis T., Schwartz Ira B. SIAM Journal on Applied Mathematics . 1999,第4期

机译：大型耦合结构/机械系统的动力学：奇摄动/适当正交分解方法
3. A New Approach of Detecting Chaos in Deterministic Dynamical System [J] . Vincenzo Niola, Giuseppe Quaremba International Journal of Applied Engineering Research . 2016,第18aPta4期

机译：确定性动力学系统中检测混沌的新方法
4. A singular value decomposition approach to detect chaotic dynamics [C] . Baglio, S., Fortuna, . 1993

机译：一种检测混沌动力学的奇异值分解方法
5. Dynamical systems approach to one-dimensional spatiotemporal chaos: A cyclist's view. [D] . Lan, Yueheng. 2004

机译：动力系统解决一维时空混乱：骑车人的观点。
6. Boolean network model for GPR142 against Type 2 diabetes and relative dynamic change ratio analysis using systems and biological circuits approach [O] . Aman Chandra Kaushik, Shakti Sahi 2015

机译：针对2型糖尿病的GPR142布尔网络模型以及使用系统和生物回路方法的相对动态变化比分析
7. EEG Signal Discrimination using Non-linear Dynamics in the EMD Domain S. M. Shafiul Alam,S. M. Shafiul Alam,Aurangozeb, and Syed TarekShahriar Abstract—An EMD-chaos based approach is proposed todiscriminate EEG signals corresponding to healthy persons,and epileptic patients during seizure-free intervals and seizureattacks. An electroencephalogram (EEG) is first empiricallydecomposed to intrinsic mode functions (IMFs). The nonlineardynamics of these IMFs are quantified in terms of the largestLyapunov exponent (LLE) and correlation dimension (CD).This chaotic analysis in EMD domain is applied to a large groupof EEG signals corresponding to healthy persons as well asepileptic patients (both with and without seizure attacks). It isshown that the values of the obtained LLE and CD exhibitfeatures by which EEG for seizure attacks can be clearlydistinguished from other EEG signals in the EMD domain.Thus, the proposed approach may aid researchers in developingeffective techniques to predict seizure activities. Index Terms—Electroencephalogram (EEG), empiricalmode decomposition (EMD), largest Lyapunov exponent (LLE),correlation dimension (CD), epileptic seizures. The Authors are with the Electrical and Electronic EngineeringDepartment, Bangladesh University of Engineering and Technology,Dhaka-1000, Bangladesh (e-mail: imamul@eee.buet.ac.bd) PDF Cite: S. M. Shafiul Alam,S. M. Shafiul Alam,Aurangozeb, and Syed Tarek Shahriar, "EEG Signal Discrimination using Non-linear Dynamics in the EMD Domain," International Journal of Computer and Electrical Engineering vol. 4, no. 3, pp. 326-330, 2012. PREVIOUS PAPER Perception of Emotions Using Constructive Learningthrough Speech NEXT PAPER Physical Layer Impairments Aware OVPN Connection Selection Mechanisms Copyright © 2008-2013. International Association of Computer Science and Information Technology Press (IACSIT Press) [O] . S. M. Shafiul Alam, Syed TarekShahriar 2012

机译：EEG信号在EMD域S. S. Shafiul Alam，S中的非线性动力学使用非线性动力学。 M. Shafiul Alam，Aurangozeb和Syed Tarekshahriar摘要 - 基于EMD Chaos的方法，提出了对应于健康人的EEG信号，癫痫发作期间的癫痫患者和Seizureattacks。脑电图（EEG）首先被凭经上分解为内在模式功能（IMF）。这些IMF的非线性动力学在最大范围的指数（LLE）和相关尺寸（CD）方面是量化的。本域中的混沌分析应用于与健康人相对应的大型脑电图（Asepileptic患者）（两者都有癫痫发作）。因此，所获得的LLE和CD表展的价值可以从EMD领域的其他EEG信号中清晰地区分脑电图的表达展示。本拟议的方法可以帮助研究人员以预测癫痫发作的癫痫发作技术。索引术语 - 脑电图（EEG），仿真态分解（EMD），最大的Lyapunov指数（LLE），相关维度（CD），癫痫发作。作者与电气电子和电子工程公司，孟加拉国工程和技术大学，孟加拉国达卡 - 1000（电子邮件：imamul@eee.buet.ac.bd）pdf cite：s. m. shafiul Alam，s。 M. Shafiul Alam，Aurangozeb和Syed Tarek Shahriar，“EEG信号歧视在EMD领域的非线性动态，”计算机电气工程卷国际杂志。 4，不。 3，pp。326-330,2012，上一篇论文对情绪的看法，使用建设性的学习言论下一篇论文物理层障碍意识到OVPN连接选择机制版权所有©2008-2013。国际计算机科学与信息技术协会出版社（IACSIT Press）
8. Evaluation of a Singular Value Decomposition Approach for Impact Dynamic Data Correlation [R] . Horta, Lucas G., Lyle, Karen H., Lessard, Wendy B. 2003

机译：冲击动态数据相关的奇异值分解方法评价

A singular value decomposition approach to detect chaos innonlinear circuits and dynamic systems

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