ISSN 0869-6632 (Online)
ISSN 2542-1905 (Print)

Review of Actual Problems of Nonlinear Dynamics

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.

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.

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.

Mathematical theory of dynamical chaos and its applications: review part 1. Pseudohyperbolic attractors

We consider important problems of modern theory of dynamical chaos and its applications. At present, it is customary to assume that in the finite-dimensional smooth dynamical systems three fundamentally different forms of chaos can be observed.

Simple electronic chaos generators and their circuit simulation

Topic and aim. The aim of the work is to review circuits of chaos generators, those described in the literature and some original ones, in a unified style basing on circuit simulations with the NI Multisim package, which makes the comparison of the various devices apparent. Investigated models.