Lyapunov exponents are a set of fundamental dynamical invariants characterizing a system's sensitive dependence on initial conditions. For more than a decade, it has been claimed that the exponents computed from electroencephalogram (EEG) or electrocorticogram (ECoG) signals can be used for prediction of epileptic seizures minutes or even tens of minutes in advance. The purpose of this paper is...

a long time ago, since the launch of the first artificial satellite in 1957, controling attitude of satellites has been considered by the designers and engineers of aerospace industry. considering the importance of this issue various methods of control in response to this need have been presented and analyzed until now. in this paper, we propose and analyze a three-axis optimal control on the s...

We show that different ways of extracting time scales from time-dependent velocity structure functions lead to different dynamic-multiscaling exponents in fluid turbulence. These exponents are related to equal-time multiscaling exponents by different classes of bridge relations which we derive. We check this explicitly by detailed numerical simulations of the GOY shell model for fluid turbulenc...

The Lyapunov, Bohl and Perron exponents belong to the most important numerical characteristics of dynamical systems used in control theory. Properties of the first two characteristics are well described in the literature. Properties of the Perron exponents are much less investigated. In this paper we show an example of two-dimensional discrete-time linear system with bounded coefficients for wh...

The question of the integrability of the mixmaster model of the Universe, presented as a dynamical system with finite degrees of freedom, is investigated in present paper. As far as the model belongs to the class of pseudo-Euclidean generalized Toda chains [1], the method of getting Kovalevskaya exponents developed in [2] for chains of Euclidean type, is used. The generalized formula of Adler a...

Lyapunov exponents of a dynamical system give information about its long-term evolution. Exponents estimation is not an easy task; it is computationally costly and, in presence of chaotic dynamics, it exhibits numerical difficulties. In a previous paper, the authors proposed an algorithm for Lyapunov exponents estimation in piecewise linear systems that strongly reduces the computational time. ...

We derive whole series of new integral inequalities of the Hardy-type, with non-conjugate exponents. First, we prove and discuss two equivalent general inequa-li-ties of such type, as well as their corresponding reverse inequalities. General results are then applied to special Hardy-type kernel and power weights. Also, some estimates of weight functions and constant factors are obtained. ...