A. Yu. Loskutov

Mechanism of Fermi acceleration in dispersing billiards with time-dependent boundaries

The paper is devoted to the problem of Fermi acceleration in Lorentz-type dispersing billiards whose boundaries depend on time in a certain way. Two cases of boundary oscillations are considered: the stochastic case, when a boundary changes following a random function, and a regular case with a boundary varied according to a harmonic law. Analytic calculations show that the Fermi acceleration takes place in such systems. The first and second moments of the velocity increment of a billiard particle, alongside the mean velocity in a particle ensemble as a function of time and number of collisions, have been investigated. Velocity distributions of particles have been obtained. Analytic and numerical calculations have been compared.

A Study of the Regularities in Solar Magnetic Activity by Singular Spectral Analysis

The method of singular spectral analysis (SSA) is described and used to analyze the series of Wolf numbers that characterizes solar activity from 1748 until 1996. Since this method is relatively new, we detail its algorithm as applied to the data under study. We examine the advantages and disadvantages of the SSA method and the conditions for its applicability to an analysis of the solar-activity data. Certain regularities have been found in the dynamics of this series. Both short and long (80–100-year) periodicities have been revealed in the sunspot dynamics. We predict the solar activity until 2014.

Oscillatory traveling waves in excitable media

A new type of waves in an excitable medium, characterized by oscillatory profile, is described. The excitable medium is modeled by a two-component activator-inhibitor system. Reaction-diffusion systems with diagonal and cross diffusion are examined. As an example, a front (kink) represented by a heteroclinic orbit in the phase space is considered. The wave shape and velocity are analyzed with the use of exact analytical solutions for wave profiles.

Suppression of chaos by cyclic parametric excitation in two-dimensional maps

We study the qualitative change of the dynamics of a generalized two-dimensional quadratic map under the influence of parametric perturbations which operate in the chaotic parameter set. It is shown that such perturbations can lead to the suppression of chaos and appearance of a regular (periodic) behaviour. Numerically we can argue that the suppression of chaos due to the parametric excitation is caused by a shift of the windows of periodic behaviour in the bifurcation diagram.

Wavelet Analysis of Fine-Scale Structures in the Saturnian B and C Rings Using Data from the Cassini Spacecraft

A continuous wavelet transform with a complex Morlet basis offers an effective method for the analysis of an instant variable periodicity in the spatially inhomogeneous matter density in the radial structure of Saturn’s rings. An original algorithm that reduces the integral transform to solving a Cauchy problem for a partial differential equation is used for an analysis of the images of Saturn’s B and C rings, which were obtained in the second half of 2004 from the Cassini spacecraft. This paper is a continuation of our preceding study of the fine-scale structure of Saturn’s rings reported in Zh. Éksp. Teor. Fiz. 128, 752 (2005) [JETP 101, 646 (2005)].

Detection of cardiac pathologies using dimensional characteristics of RR intervals in electrocardiograms

The possibility of detecting pathologies in patients with various types of heart failure by analyzing the correlation dimension and embedding dimension of RR intervals in electrocardiograms is estimated. Limitations of the proposed approach and methods of overcoming them are discussed. It is demonstrated that these methods are suitable for provisional diagnosis.

Suppression of chaos in the vicinity of a separatrix

The standard Melnikov method for analyzing the onset of chaos in the vicinity of a separatrix is used to explore the possibility of suppressing chaos of dynamical systems of a certain class. Analytical expressions are obtained for external perturbations that eliminate chaotic behavior. These results are supplemented with a numerical analysis of the Duffing-Holmes-oscillator and pendulum equations.

Stabilization of chaotic oscillations in systems with a hyperbolic-type attractor

AstractIt has been shown that the chaotic dynamics of systems with nearly hyperbolic-type attractors can be stabilized by periodic parametric perturbations.

New approach to the defibrillation problem: Suppression of the spiral wave activity of cardiac tissue

A model of an excitable medium is considered for describing the development of fibrillation (i.e., spatiotemporal chaos) in cardiac tissue through the generation of a set of coexisting spiral waves. It is shown that a weak external point action on such a medium leads to the suppression of all spiral waves and, correspondingly, to the stabilization of the system dynamics. After reaching the regular regime, only the external source exists in the medium. The frequencies and amplitudes at which such stabilization occurs are determined. The case of the action of several point sources is considered. Analysis is performed using the Bray method to identify the number of spiral waves.

Analysis of small-scale wave structures in the saturnian a ring based on data from the cassini interplanetary spacecraft

The images obtained during the second half of 2004 by the Cassini interplanetary spacecraft are analyzed. The method of analysis is based on the original algorithm of a continuous wavelet transform with a complex Morlet wavelet that reduces the integral transform to solving a Cauchy problem for a system of partial differential equations. This method is shown to be a fairly efficient tool for analyzing the instant variable periodicity of the spatial particle inhomogeneity in the radial structure of Saturn’s rings.