# хаос

## Chaotic microwave pulse train generation in self-oscillatory system based on a ferromagnetic film

Experimental investigations results of the ring self-oscillatory system based on a ferromagnetic ?lm at three-wave interactions were considered. The model describing this system was constructed. The typical regimes of a generation, including generation of the chaotic microwave train were calculated with the help of the constructed model. The numerical simulations and experimental results had a good agreement.

## Parametric generators with chaotic amplitude dynamics corresponding to attractors of smale–williams type

A new approach is considered to design of parametric generators of chaos with hyperbolic attractors on the basis of two alternately excited subsystems, each consisting of three oscillators, one of which plays the role of the pump source. In contrast to previously proposed schemes, the angular variable undergoing a multiple increase over each characteristic period is a quantity characterizing the amplitude ratio of two oscillators, rather then the phase of successive oscillation trains.

## Numerical simulation of nonlinear dynamics in multiple cavity klystron oscillator with delayed feedback by the "partikle-in- cell» method

The 1.5 D code program of numerical simulation of nonlinear nonstationary processes in the klystron-type devices based on the nonstationary L.A. Vainshtein’s theory of cavity excitation and the «particle-in-cell» method for modeling of the electron beam dynamics is developed. The results of numerical simulation of the basic oscillation modes of the fourcavity klystron oscillator with the external delayed feedback are presented.

## Analysis of stochastic work of the composite voltage stabilizer consisting of two buck converters connected as master–slave by fractal measures of deterministic chaos.

Stochastic operation of the parallel–connected buck convertors is considered. For qualitative analysis of the system the bifurcation diagrams are plotted. Quantitative analysis of chaotic regimes was realized by computing of main and special fractal dimensions.

## Chaos in radio device with squarelaw phase modulator and interference amplification of quasiharmonic signal: a model and simulation

The attempt is undertaken to define a class of oscillations or waves sources, the operation principle of which is based on interference amplification of feedback signal by an input signal. The precedent here is the optical Ikeda’s system. The radioelectronic analog of a nonlinear ring interferometer and it modification are offered, the block diagrams and mathematical models are constructed. The computer simulation is performed. An intermittency, chaos, regular, static modes are detected.

## Experiments with a source of chaos – a radioelectronic device with squarelaw phase modulator and interference amplification of quasiharmonic signal

A modified radioelectronic analog of the nonlinear ring cavity is realized in laboratory. The device represents a special class of oscillations or waves sources. An operation principle of the sources is based on interference amplification of feedback signal by an input signal. A laboratory experiments are performed, the likeness of their results and simulation data is shown. An intermittency, chaos, regular, static modes are detected. A thesis on controlled nonlinearity of dynamical systems is suggested.

## Dynamic modes of twoage population model

In this paper we research a mathematical model of dynamics for the population number. We considered the population of the twoage classes by the beginning of the next season: the younger, one including not reproductive individuals, and the senior class, consisting of the individuals participating in reproduction. The model parameters (birth rate and survival rates) represent the exponential functions of the both age groups numbers. According to this supposition the densitydependent factors restrict the development of population. Analytical and numerical analysis of the model is made.

## Temperature effect on drift velocity of electrons in superlattice in electric and tilted magnetic fields

The work studies the effects of temperature on drift velocity of the electrons in semiconductor superlattices in electric and tilted magnetic fields. It is shown that a thermal distribution of the electrons can counterintuitively enhance the phenomena related to resonances between the Bloch and the cyclotron frequencies of electron motion in superlattices. In particular, the increase of temperature leads to more prominent resonant maxima in the dependence of drift velocity of electrons on the strength of an electric field.

## Stabilization of chaos in the rossler system by pulsed or harmonic signal

The stabilization of chaos in the Rossler system by external signal is investigated. Different types of external action are considered: both of pulsed and harmonic signal. There are illustrations: charts of dynamical regimes, phase porters, stroboscopic section of Poincare, spectrum of Lyapunov exponents. Comparative analysis of efficiency of stabilization of band chaos and spiral chaos by different signal is carried out. The dependence of synchronization picture on direction of acting pulses is shown.

## On the way towards multidimensional tori

The problem of the dynamics of three coupled selfoscillators and three coupled periodically driven selfoscillators is discussed, in the last case only one of the oscillators is directly exited by the external fore. The regions of complete synchronization, two, threeand fourfrequency tori and chaos are revealed. Three typical situations of synchronization of three selfoscillators by the external driving are found. First situation refers to the mode locking of autonomous oscillators. Two other situations refer to quasiperiodic dynamics in the coupled autonomous oscillators.