We prove that under certain basic regularity conditions, a random iteration of logistic maps converges to a random point attractor when the Lyapunov exponent is negative, and does not converge to a point when the Lyapunov exponent is positive.

OBJECTIVE To investigate the nature of variability present in time series generated from gait parameters of two different age groups via a nonlinear analysis. DESIGN Measures of nonlinear dynamics were used to compare kinematic parameters between elderly and young females. BACKGROUND Aging may lead to changes in motor variability during walking, which may explain the large incidence of fall...

For strongly monotone dynamical systems on a Banach space, we show that the largest Lyapunov exponent [Formula: see text] holds shy set in measure-theoretic sense. This exhibits admit no observable chaos, notion of which was formulated by L.S. Young. We further such phenomenon chaos is robust under text]-perturbation systems.

Common noise acting on a population of identical oscillators can synchronize them. We develop a description of this process which is not limited to the states close to synchrony, but provides a global picture of the evolution of the ensembles. The theory is based on the WatanabeStrogatz transformation, allowing us to obtain closed stochastic equations for the global variables. We show that at t...

In this work we present a theoretical and numerical study of the behaviour of the maximum Lyapunov exponent for a generic coupled-map-lattice in the weak-coupling regime. We explain the observed results by introducing a suitable continuous-time formulation of the tangent dynamics. The first general result is that the deviation of the Lyapunov exponent from the uncoupled-limit limit is function ...

One of the inherent weaknesses of the EEG signal processing is noises and artifacts. To overcome it, some methods for prediction of epilepsy recently reported in the literature are based on the evaluation of chaotic behavior of intracranial electroencephalographic (EEG) recordings. These methods reduced noises, but they were hazardous to patients. In this study, we propose using Lyapunov spectr...

We study the Hausdorff dimension spectrum for Lyapunov exponents for a class of interval maps which includes several non-hyperbolic situations. We also analyze the level sets of points with given lower and upper Lyapunov exponents and, in particular, with zero lower Lyapunov exponent. We prove that the level set of points with zero exponent has full Hausdorff dimension, but carries no topologic...

In 1892, the general problem of stability by the first approximation was considered by Lyapunov. He proved that if the system of the first approximation is regular and all its Lyapunov exponents (or characteristic exponents) are negative, then the solution of the original system is asymptotically Lyapunov stable. In 1930, it was stated by O. Perron that the requirement of regularity of the firs...

In a previous paper [6] we suggested a numerical method for computing all Lyapunov exponents of a dynamical system by spatial integration with respect to an ergodic measure. The method extended an earlier approach of Aston and Dellnitz [2] for the largest Lyapunov exponent by integrating the diagonal entries from the QR-decomposition of the Jacobian for an iterated map. In this paper we provide...