# Обзоры актуальных проблем нелинейной динамики

## Patterns in excitable dynamics driven by additive dichotomic noise

Pattern formation due the presence of additive dichotomous fluctuations is studied an extended system with diffusive coupling and a bistable FitzHugh–Nagumo kinetics. The fluctuations vary in space and/or time being noise or disorder, respectively. Without perturbations the dynamics does not support pattern formation. With proper dichotomous fluctuations, however, the homogeneous steady state is destabilized either via a Turing instability or the fluctuations create spatial nuclei of an inhomogeneous states.

## Fractional diffusion equation for aging and equilibrated random walks

We consider continuous time random walks and discuss situations pertinent to aging. These correspond to the case when the initial state of the system is known not at preparation (at t = 0) but at the later instant of time t1 > 0 (intermediatetime initial condition).

## Entropy and forecasting of time series in the theory of dynamical systems

A contemporary consideration of such concepts as dimension and entropy of dynamical systems is given. Description of these characteristics includes into the analysis the other notions and properties related to complicated behavior of nonlinear systems as embedding dimension, prediction horizon etc., which are used in the paper. A question concerning the application of these ideas to real observables of the economical origin, i.e. market prices of the companies Schlumberger, Deutsche Bank, Honda, Toyota, Starbucks, BP is studied.

## Self-sustained oscillations in quasiharmonic and chaotic oscillators in the presence of fluctuations

The paper presents the results of the classical theory of fluctuations in the quasiharmonic van der Pol oscillator. Stochastic equations for amplitude and phase of selfsustained oscillations are formulated and then their solutions are analyzed. The autocorrelation function and power spectrum of noisy selfsustained oscillations are studied. Then the spectral and correlations characteristics of chaotic selfsustained oscillations are numerically analyzed in spiral chaos oscillators.

## Ultrawideband wireless sensor networks based on chaotic radiopulses

Wireless sensor networks that is a fast emerging branch of modern telecommunications are considered in this paper. Particular attention is paid on ultrawideband sensor networks where chaotic radiopulses are used as an information carrier between sensor nodes. Development of such wireless sensor networks became possible after longterm investigations of chaotic oscillations and chaos control.

## Two-stream instability – linear and nonlinear microwave phenomena

This article is the first of two parts of the review devoted to the phenomenon of two-beam instability in microwave electronics. The main goal is to cover as much as possible the most complete list of papers on various models and methods of analysis of the two-beam instability. The first part contains papers which, in our view, most fully describe the development of ideas of two-stream instability in microwave electronics.

## Two-stream instability – linear and nonlinear microwave phenomena

This article is the second part of the review of works devoted to the phenomenon of two-stream instability in microwave electronics. As it is known, a problem of creating devices operating in the terahertz frequency range is a rather actual today. Although there are many devices that can generate or amplify signals in this range, most of them refer to extremely powerful relativistic devices. At the same time there is a lack of compact medium power devices.

## Turbulence in microwave electronics: teoretical approaches and experimental results

A review of the current state of different theoretical approaches to the description of turbulence in electron beams and electronic devices at microwave frequencies is shown. A three types of turbulent (nonlaminar) electron beams were considered. The first type of turbulent electron beam is caused by the intersection of electronic trajectories (e.g., due to thermal velocity) and it is common to the flow of electrons at all.

## Polynomial eigenfuctions of the perron–frobenius operator

In the paper, we reveal the structure of polynomial functions of the eigenfunctions and the kernel of the Perron–Frobenius operator for one-dimensional chaotic maps that iterative functions have the following properties: they are piecewise-linear ones; they have full branches transforming the domain of its definition to the full range of the mapping; the have arbitrary slope of branches; they have not some gaps between the branches.

## Wavelet transform of time series and atmosphere dynamics

Wavelet transform is described as a new tool for investigation of data generated by the chaotic dynamic systems. Its usage is illustrated by the analysis of the temporal oscillation of the atmosphere zonal circulation index.