The Largest Lyapunov Exponent of Dynamical Systems with time Delay

机译：具有时间延迟的动态系统最大的Lyapunov指数

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We show that the largest Lyapunov exponent of the dynamical system with time delay can be estimated by the procedure based on the phenomenon of chaos synchronization. Our approach can be applied both for flow and discrete maps.

机译：我们表明，基于混沌同步现象的过程，可以估算具有时间延迟的动态系统的最大Lyapunov指数。我们的方法可以应用于流程和离散地图。

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《IUTAM Symposium on Chaotic Dynamics and Control of Systems and Processes in Mechanics》|2005年||共8页
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A. Stefanski; T. Kapitaniak; A. Dabrowski;
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中图分类 O3-532;
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Lyapunov exponents; chaos synchronization; systems with delay;

机译：Lyapunov指数;混沌同步;有延迟的系统;

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专利

1. Evaluation of the largest Lyapunov exponent in dynamical systems with time delay [J] . Stefanski A, Dabrowski A, Kapitaniak T Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science . 2005,第5期

机译：时滞动力系统中最大Lyapunov指数的评估
2. Two-Sided Bounds for the Largest Lyapunov Exponent and Exponential Stability Criteria for Nonlinear Systems with Arbitrary Delays [J] . A. A. Zevin, S. Yu. Poslavskii Automation and Remote Control . 2012,第1期

机译：最大Lyapunov指数的两面界和任意时滞非线性系统的指数稳定性准则。
3. LYAPUNOV EXPONENTS AND OSELEDETS DECOMPOSITION IN RANDOM DYNAMICAL SYSTEMS GENERATED BY SYSTEMS OF DELAY DIFFERENTIAL EQUATIONS [J] . Communications on pure and applied analysis . 2020,第4期

机译：Lyapunov指数和OSELEDETS在延迟微分方程系统产生的随机动力系统中分解
4. The Largest Lyapunov Exponent of Dynamical Systems with time Delay [C] . A. Stefanski, T. Kapitaniak, A. Dabrowski IUTAM Symposium on Chaotic Dynamics and Control of Systems and Processes in Mechanics . 2005

机译：具有时间延迟的动态系统最大的Lyapunov指数
5. Lyapunov exponents and persistence in dynamical systems with applications to some discrete time models [D] . Salceanu, Paul Leonard 2009

机译：动态系统中的Lyapunov指数和持久性及其在某些离散时间模型中的应用
6. OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS [O] . WILLIAM OTT, MAURICIO A. RIVAS, JAMES WEST -1

机译：观察无限维动力系统的Lyapunov指数
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）

The Largest Lyapunov Exponent of Dynamical Systems with time Delay

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