Error analysis of QR algorithms for computing Lyapunov exponents [PDF]
, 2001 Lyapunov exponents give valuable information about long term dynamics. The discrete and continuous QR algorithms are widely used numerical techniques for computing approximate Lyapunov exponents, although they are not yet supported by a general error ...
McDonald, E.J., Higham, D.J.
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Analysis for global characteristics of Lyapunov exponents in vehicle plane motion system
Scientific Reports, 2022 In the field of vehicle system dynamics, it is significant to propose an appropriate quantitative indicator for system stability or dynamics characteristics.
Fanyu Meng +4 more
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Analysis of Lyapunov Method for Control of Quantum States [PDF]
IEEE Transactions on Automatic Control, 2010 The natural trajectory tracking problem is studied for generic quantum states represented by density operators. A control design based on the Hilbert-Schmidt distance as a Lyapunov function is considered. The control dynamics is redefined on an extended space where the LaSalle invariance principle can be correctly applied even for non-stationary target
Xiaoting Wang, Sophie G. Schirmer
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Determining the domain of attraction of hybrid non–linear systems using maximal Lyapunov functions [PDF]
, 2010 summary:In this article a method is presented to find systematically the domain of attraction (DOA) of hybrid non-linear systems. It has already been shown that there exists a sequence of special kind of Lyapunov functions $V_n$ in a rational functional ...
Hangos, Katalin M. +3 more
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EEG analysis in patients with schizophrenia based on Lyapunov exponents
Informatics in Medicine Unlocked, 2020 The present work focused on study of the chaotic nature of the electroencephalogram (EEG) signal in schizophrenia by assessing Lyapunov exponents, which can serve as indicators of specific brain function suffered from the disease.
Ilya E. Kutepov +6 more
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Lyapunov spectra of chaotic recurrent neural networks
Physical Review Research, 2023 This article is part of the Physical Review Research collection titled Physics of Neuroscience. Recurrent networks are widely used as models of biological neural circuits and in artificial intelligence applications.
Rainer Engelken, Fred Wolf, L. F. Abbott
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Geometric approach to Lyapunov analysis in Hamiltonian dynamics [PDF]
Physical Review E, 2001 As is widely recognized in Lyapunov analysis, linearized Hamilton's equations of motion have two marginal directions for which the Lyapunov exponents vanish. Those directions are the tangent one to a Hamiltonian flow and the gradient one of the Hamiltonian function.
Yamaguchi, Yoshiyuki Y., Iwai, Toshihiro
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Biologically inspired adaptive intelligent secondary control for MGs under cyber imperfections
IET Cyber-Physical Systems, 2019 In this study, the authors investigate the secondary control of microgrids (MGs) in the presence of cyber imperfections such as delay and/or noise, and system disturbances.
Mohammad Jafari +6 more
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Improved Discontinuous Lyapunov Functionals for Stability Analysis of Sampled-Data Systems
IEEE Access, 2021 This paper is devoted to proposing improved discontinuous Lyapunov functionals for the stability analysis of sampled-data systems. Specifically, by relaxing the existing looped-functional, this paper makes the first attempt to integrate 1/t-tk ∫ ...
Thanh Binh Nguyen, Sung Hyun Kim
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Asymptotic behaviours of stochastic differential delay equations [PDF]
, 2006 Most of the existing results on stochastic stability use a single Lyapunov function, but we shall instead use multiple Lyapunov functions in this paper.
Shen, Yi, Mao, Xuerong
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