منابع مشابه
Maximal Lyapunov exponent at crises.
We study the variation of Lyapunov exponents of simple dynamical systems near attractor-widening and attractor-merging 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 in the value itself, in the case of the attractor-widening crisis, or in the slope, for attractor...
متن کاملAnalytical estimation of the maximal Lyapunov exponent in oscillator chains
An analytical expression for the maximal Lyapunov exponent λ1 in generalized Fermi-PastaUlam 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 the agreement is good over a wide range of energy densities ε. At very high energy density the power...
متن کاملCurvature Fluctuations and the Lyapunov exponent at Melting
We calculate the maximal Lyapunov exponent in constant-energy 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 with the total energy, but the slope changes sharply at the melting transition. In the bulk system, ...
متن کاملDiscontinuity of the Lyapunov Exponent
We study discontinuity of the Lyapunov exponent. We construct a limit-periodic Schrödinger operator, of which the Lyapunov exponent has a positive measure set of discontinuities. We also show that the limit-periodic potentials, whose Lyapunov exponent is discontinuous, are dense in the space of limit-periodic potentials.
متن کاملEstimation of the maximal Lyapunov exponent of nonsmooth systems using chaos synchronization
The maximal Lyapunov exponent of a nonsmooth system is the lower bound for the proportional feedback gain necessary to achieve full state synchronization. In this paper, we prove this statement for the general class of nonsmooth systems in the framework of measure differential inclusions. The results are used to estimate the maximal Lyapunov exponent using chaos synchronization, which is illust...
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ژورنال
عنوان ژورنال: Physical Review E
سال: 1996
ISSN: 1063-651X,1095-3787
DOI: 10.1103/physreve.53.3420