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...

We introduce a definition of a "localization width" whose logarithm is given by the entropy of the distribution of particle component amplitudes in the Lyapunov vector. Different types of localization widths are observed, for example, a minimum localization width where the components of only two particles are dominant. We can distinguish a delocalization associated with a random distribution of...

we propose a novel approach for detecting precursors to epileptic seizures in intracranial electroencephalograms (ieeg), which is based on the analysis of system dynamics. in the proposed scheme, the largest lyapunov exponent of the discrete wavelet packet transform (dwpt) of the segmented eeg signals is considered as the discriminating features. such features are processed by a support vector ...

In this work, we propose a method of control and anti-control chaos based on the moving largest Lyapunov exponent using reinforcement learning. method, design reward function for learning according to exponent, which is similar average but computes corresponding recently updated time series with fixed, short length. We adopt density peaks-based clustering algorithm determine linear region diver...

The loss of complexity in ageing hypothesis (LOCH) has found support from EEG studies, most which adopted signal-domain measures. present study the largest Lyapunov exponent (LLE) to measure a nonlinear dynamical systems perspective. A total 144 participants were included and divided into young, young-old old-old groups. Both sensor-space source-space results showed significantly lower LLE for ...

We investigate thermalization processes occurring at different time scales in the Yang-Mills-Higgs system at high temperatures. We determine the largest Lyapunov exponent associated with the gauge fields and verify its relation to the perturbatively calculated damping rate of a static gauge boson.

We investigate thermalization processes occurring at different time scales in the Yang-Mills-Higgs system at high temperatures. We determine the largest Lyapunov exponent associated with the gauge fields and verify its relation to the perturbatively calculated damping rate of a static gauge boson. 12.38.Mh, 11.15.Kc Typeset using REVTEX 1

A novel generation method of chaotic attractor is introduced in this paper. The underlying mechanism involves a simple three-dimensional time-varying system with simple time functions as control inputs. Moreover, it is demonstrated by simulation that various attractor patterns are generated conveniently by adjusting suitable system parameters. The largest Lyapunov exponent of the system has bee...