Results 221 to 230 of about 22,081,541 (270)

Lyapunov exponents, dual Lyapunov exponents, and multifractal analysis

Chaos: An Interdisciplinary Journal of Nonlinear Science, 1999
It is shown that the multifractal property is shared by both Lyapunov exponents and dual Lyapunov exponents related to scaling functions of one-dimensional expanding folding maps. This reveals in a quantitative way the complexity of the dynamics determined by such maps.
Fan, Aihua, Jiang, Yunping
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A Lyapunov approach to frequency analysis

Proceedings of the 2004 American Control Conference, 2004
This paper proposes a Lyapunov approach to frequency analysis for general systems. The notion of frequency response is extended to general systems through a connection in linear systems. Lyapunov approaches to the characterization of frequency response are established for linear systems, homogeneous systems and nonlinear systems, respectively.
Tingshu Hu, Andrew R. Teel, Zongli Lin
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Lyapunov analysis of semistability

Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251), 1999
Semistability is the property whereby the solutions of a system converge to stable equilibrium points determined by the initial conditions. Important applications of this notion of stability include lateral aircraft dynamics and the dynamics of chemical reactions.
BHAT, SP, BERNSTEIN, DENNIS S
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Lyapunov Spectral Analysis on Random Data

International Journal of Bifurcation and Chaos, 1997
In this paper, an algorithm for estimating all Lyapunov exponents, or Lyapunov spectra of deterministic dynamical systems, is applied to random time series, that is, the time intervals of gamma ray emissions of cobalt. The algorithm used in this paper is that proposed by Sano and Sawada, which estimates Jacobian matrices of an assumed dynamical system
Ikeguchi, Tohru, Aihara, Kazuyuki
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SENSITIVITY ANALYSIS AND LYAPUNOV STABILITY

IFAC Proceedings Volumes, 1964
This chapter focuses on sensitivity analysis and Lyapunov stability. Sensitivity analysis is an extension and development of a rather old idea, which became known in the theory of partial differential equations under the name of a correctly set problem.
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Sensitivity Analysis of Generalized Lyapunov Equations

2005
The sensitivity of generalized matrix Lyapunov equations relative to perturbations in the coefficient matrices is studied. New local and non-local perturbation bounds are obtained.
Michail M. Konstantinov, Petko Hr. Petkov, Nikolai D. Christov   +2 more
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A Lyapunov analysis of accelerated methods in optimization

J. Mach. Learn. Res., 2021
Summary: Accelerated optimization methods, such as Nesterov's accelerated gradient method, play a significant role in optimization. Several accelerated methods are provably optimal under standard oracle models. Such optimality results are obtained using a technique known as ``estimate sequences,'' which yields upper bounds on convergence properties ...
Ashia C. Wilson, Ben Recht, Michael I. Jordan   +2 more
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Lyapunov stability analysis of a model describing hematopoiesis

2015 European Control Conference (ECC), 2015
The knowledge of Lyapunov-Krasovskii functionals offers strong advantages when investigating the local or global stability properties of equilibrium points of a system with delay. Unfortunately, in many cases the construction of these functionals is not an easy task.
Djema, Walid, Mazenc, Frédéric, Bonnet, Catherine   +2 more
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A Lyapunov approach to analysis of discrete singular systems

Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228), 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, QL, Hill, D, Liu, WQ
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Multifractal analysis of the Lyapunov spectrum

Chaos, Solitons & Fractals, 2002
The multifractal spectrum of Lyapunov exponents is studied under a weaker hypotesis on dynamical systems than in earlier papers. Namely, instead of imposing expanding or Axiom A assumptions on a diffeomorphism \(f\) in question the authors assume just expansivity, specification and the Bowen condition on \(\phi=\|Df\|\) which ensures existence and ...
Mesón, Alejandro M., Vericat, Fernando
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