This paper deals with the problem of the discrimination between wellpredictable and not-well-predictable time series. One criterion for the separation is given by the size of the Lyapunov exponent, which was originally defined for deterministic systems. However, the Lyapunov exponent can also be analyzed and used for stochastic time series. Experimental results illustrate the classification bet...

We investigate a control of chaotic solitons using a modified time-delayed autosynchronization method. Numerical results for the maximal Lyapunov exponent are in very good agreement with analytical theory developed originally for low-dimensional systems. The control is most efficient when the spatial distribution of the control force is proportional to the kink translational mode. Observations ...

Fingertip pulsations (plethysmograms) were found to obey chaotic dynamics [1]. We applied chaos theory to analysis of the time series of plethysmograms under various human physio-psychological conditions. It found out that the largest Lyapunov exponent of the time series could be used to characterize physio-psychological status. A visual representation method based on constellation graphs was d...

We introduce a “spatial” Lyapunov exponent to characterize the complex behavior of non chaotic but convectively unstable flow systems. This complexity is of spatial type and is due to sensitivity to the boundary conditions. We show that there exists a relation between the spatial-complexity index we define and the comoving Lyapunov exponents. In these systems the transition to chaos, i.e. the a...

Based on Lyapunov-exponent generation and the Gram-Schimdt orthogonalization, analysis and design of some anti-controlled higher-dimensional hyperchaotic systems are investigated in this paper. First, some theoretical results for Lyapunov-exponent generating algorithms are proposed. Then, the relationship between the number of Lyapunov exponents and the number of positive real parts of the eige...

We study the effect of a random perturbation on a one-parameter family of dynamical systems whose behavior in the absence of perturbation is ill understood. We provide conditions under which the perturbed system is ergodic and admits a positive Lyapunov exponent, with an explicit lower bound, for a large and controlled set of parameter values. Acknowledgements. The authors are indebted to Lai-S...

Numerical experiments reveal that estimates of the Lyapunov exponent for the logistic map x t+1 = f(x t) = 4x t (1 ? x t) are anomalously precise: they are distributed with a standard deviation that scales as 1=N, where N is the length of the trajectory, not as 1= p N, the scaling expected from an informal interpretation of the central limit theorem. We show that this anomalous convergence foll...

In this article, we propose a class of high-order stochastic partial differential equations (SPDEs) for spatial dimensions d ≤ 5 which might be called high-order stochastic Anderson models. This class of the equations is perturbed by a space-time white noise when d ≤ 3 and by a space-correlated Gaussian noise when d = 4, 5. The objectives of this article are to get some estimates on the Lyapuno...

A positive Lyapunov exponent is one practical deÞnition of chaos. We develop a formal test for chaos in a noisy system based on the consistent standard errors of the nonparametric Lyapunov exponent estimators. When our procedures are applied to international real output series, the hypothesis of the positive Lyapunov exponent is signiÞcantly rejected in many cases. One possible interpretation o...

I develop an improved Hamiltonian for classical, Minkowski Yang-Mills theory, which evolves infrared fields with corrections from lattice spacing a beginning at O(a). I use it to investigate the response of Chern-Simons number to a chemical potential, and to compute the maximal Lyapunov exponent. Both quantities have small a limits, in both cases within 10% of the limit found using the unimprov...