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Maximal Lyapunov exponent at crises
 Phys. Rev. E
, 1996
"... We study the variation of Lyapunov exponents of simple dynamical systems near attractorwidening and attractormerging crises. The largest Lyapunov exponent has universal behaviour, showing abrupt variation as a function of the control parameter as the system passes through the crisis point, either ..."
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Cited by 1 (0 self)
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at a widening crisis. In this paper, we study the behaviour of the Lyapunov exponent in systems where there are abrupt changes in the dynamics as a parameter is varied. Our interest is in exploring the typical dependence of the maximal Lyapunov exponent (MLE) on the control parameter so as to elucidate
The Maximal Lyapunov Exponent of a Time Series
, 2009
"... Techniques from dynamical systems have been applied to the problem of predicting epileptic seizures since the early 90’s. In particular, the computation of Lyapunov exponents from a series of electrical brain activity has been claimed to have great success. We survey the relevant topics from pure dy ..."
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dynamical systems theory and explain how Wolf et al. adapted these ideas to the practical situation of trying to extract information from a time series. In doing so, we consider instances of time series where we may visually extract properties of the maximal Lyapunov exponent in an attempt to cultivate some
Analytical estimation of the maximal Lyapunov exponent in oscillator chains
, 2008
"... An analytical expression for the maximal Lyapunov exponent λ1 in generalized FermiPastaUlam oscillator chains is obtained. The derivation is based on the calculation of modulational instability growth rates for some unstable periodic orbits. The result is compared with numerical simulations and th ..."
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An analytical expression for the maximal Lyapunov exponent λ1 in generalized FermiPastaUlam oscillator chains is obtained. The derivation is based on the calculation of modulational instability growth rates for some unstable periodic orbits. The result is compared with numerical simulations
Determining Lyapunov Exponents from a Time Series
 Physica
, 1985
"... We present the first algorithms that allow the estimation of nonnegative Lyapunov exponents from an experimental time series. Lyapunov exponents, which provide a qualitative and quantitative characterization of dynamical behavior, are related to the exponentially fast divergence or convergence of n ..."
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Cited by 495 (1 self)
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We present the first algorithms that allow the estimation of nonnegative Lyapunov exponents from an experimental time series. Lyapunov exponents, which provide a qualitative and quantitative characterization of dynamical behavior, are related to the exponentially fast divergence or convergence
Determination of Lyapunov Exponents in Discrete Chaotic Models
, 2012
"... ABSTRACT: This paper discusses the Lyapunov exponents as a quantifier of chaos with two dimensional discrete chaotic model: F(x,y) = (y, µx+λy – y3), Where, µ and λ are adjustable parameters. Our prime objective is to find First Lyapunov exponent, Second Lyapunov exponent and Maximal Lyapunov expon ..."
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ABSTRACT: This paper discusses the Lyapunov exponents as a quantifier of chaos with two dimensional discrete chaotic model: F(x,y) = (y, µx+λy – y3), Where, µ and λ are adjustable parameters. Our prime objective is to find First Lyapunov exponent, Second Lyapunov exponent and Maximal Lyapunov
Curvature Fluctuations and the Lyapunov exponent at Melting
, 1997
"... We calculate the maximal Lyapunov exponent in constantenergy molecular dynamics simulations at the melting transition for finite clusters of 6 to 13 particles (model rare–gas and metallic systems) as well as for bulk rare– gas solid. For clusters, the Lyapunov exponent generally varies linearly wit ..."
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We calculate the maximal Lyapunov exponent in constantenergy molecular dynamics simulations at the melting transition for finite clusters of 6 to 13 particles (model rare–gas and metallic systems) as well as for bulk rare– gas solid. For clusters, the Lyapunov exponent generally varies linearly
Complex Behavior In Extended Systems: Beyond The Lyapunov Exponent
"... Introduction The widely accepted definition of chaos  and its most popular manifestation  is the sensitive dependence of the evolution on the initial conditions, i.e. a small uncertainty ffi x(0) in the initial state grows exponentially in time: jffix(t)j jffix(0)j exp( 1 t), where 1 is the m ..."
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is the maximal Lyapunov exponent 1 . The condition 1 ? 0 implies a limited predictability, that is a dynamical randomness, thefore it is a signal of an interesting behavior. However many non trivial behaviors can appear in systems which are not chaotic, i.e. with 0. Let us briefly mention the systems
Lyapunov exponents, dual Lyapunov exponents, and multifractal analysis
"... It is shown that the multifractal property is shared by both Lyapunov exponents and dual Lyapunov exponents related to scaling functions of onedimensional expanding folding maps. This reveals in a quantitative way the complexity of the dynamics determined by such maps. © 1999 American Institute of ..."
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lives becomes important. The multifractal analysis provides us with a tool to conduct this study. In this article, we use the Lyapunov exponent and the dual Lyapunov exponent for such a given dynamical system to give some multifractal decompositions for the maximal invariant set and the dual symbolic
The Lyapunov Characteristic Exponents and their
 Computation, Lect. Notes Phys
, 2010
"... For want of a nail the shoe was lost. For want of a shoe the horse was lost. For want of a horse the rider was lost. For want of a rider the battle was lost. For want of a battle the kingdom was lost. And all for the want of a horseshoe nail. For Want of a Nail (proverbial rhyme) Summary. We present ..."
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Cited by 29 (2 self)
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present a survey of the theory of the Lyapunov Characteristic Exponents (LCEs) for dynamical systems, as well as of the numerical techniques developed for the computation of the maximal, of few and of all of them. After some historical notes on the first attempts for the numerical evaluation of LCEs, we
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