A. E. Khramov

Wavelet Bicoherence Analysis as a Method for Investigating Coherent Structures in an Electron Beam with an Overcritical Current

Results are presented from numerical modeling of the effect of the inhomogeneity of the ion background on the complicated spatiotemporal dynamics of an electron beam with a virtual cathode in plane geometry. The possibility is demonstrated of increasing the generation frequency without changing the beam current. The spatiotemporal structures that form in the beam and govern the complicated stochastic dynamics of the nonuniform electron-plasma system under consideration are investigated by the methods of wavelet bicoherence and by analyzing the calculated electron trajectories on the space-time diagrams.

The effect of temperature on the nonlinear dynamics of charge in a semiconductor superlattice in the presence of a magnetic field

The space-time dynamics of electron domains in a semiconductor superlattice is studied in a tilted magnetic field with regard to the effect of temperature. It is shown that an increase in temperature substantially changes the space-time dynamics of the system. This leads to a decrease in the frequency and amplitude of oscillations of a current flowing through the semiconductor superlattice. The quenching of oscillations is observed, which is attributed to the change in the drift velocity as a function of electric-field strength under the variation of temperature.

Behavior of Dynamical Systems in the Regime of Transient Chaos

The transient chaos regime in a two-dimensional system with discrete time (Eno map) is considered. It is demonstrated that a time series corresponding to this regime differs from a chaotic series constructed for close values of the control parameters by the presence of “nonregular” regions, the number of which increases with the critical parameter. A possible mechanism of this effect is discussed.

Developmental Changes in the Frequency-Time Structure of Sleep Spindles on the EEG in Rats with a Genetic Predisposition to Absence Epilepsy (WAG/Rij)

Sleep spindles are known to form spontaneously in the thalamocortical system during slow-wave sleep; pathological processes in the thalamocortical network may be the cause of absence epilepsy. The aim of the present work was to study developed changes in the frequency-time structure of sleep spindles during the progressive development of absence epilepsy in WAG/Rij rats. EEG recordings were made at age 5, 7, and 9xa0months using epidural electrodes implanted into the frontal cortex. Automatic recognition and subsequent analysis of sleep spindles on the EEG were performed using continuous wavelet transformation analysis. The duration of epileptic discharges and the total duration of epileptic activity were found to increase with age, while the duration of sleep spindles, conversely, decreased. In terms of mean frequency, sleep spindles could be divided into three classes: “slow” (mean frequency 9.3xa0Hz), “transitional” (11.4xa0Hz), and “fast” (13.5xa0Hz). Slow and transitional spindles in five-month-old animals showed increases in frequency from the beginning of the spindle to the end. The more intense the epilepsy, the shorter the durations of spindles of all types. The mean frequencies of “transitional” and “fast” spindles were higher in rats with more intense signs of epilepsy. Overall, high epileptic activity in WAG/Rij rats was linked with significant changes in spindles of the transitional type, with less marked changes in the two traditionally identified types of spindle, slow and fast.

Generalized synchronization and noise-induced synchronization: The same type of behavior of coupled chaotic systems

At present, the study of peculiarities of synchronization of coupled chaotic oscillators seems to be a substantial and topical direction of theoretical and experimental research, which is of particular practical importance in analysis and diagnostics of medical and physiological data, information security, and control of radiophysical and laser systems [1–3]. Currently, different types of chaotic synchronization are distinguished; each of them has its own features and methods for detection [1]. It is also important to find and analyze common regularities of chaotic synchronization, which requires establishment of the relationship between its different types. In particular, the results presented in [4, 5] demonstrate that different types of chaotic synchronization in flow systems with a few degrees of freedom may be reduced to time scale synchronization.

Adaptive wavelets applied to the analysis of nonlinear systems with chaotic dynamics

We consider an approach to the analysis of nonstationary processes based on the application of wavelet basis sets constructed using segments of the analyzed time series. The proposed method is applied to the analysis of time series generated by a nonlinear system with and without noise.

Experimental and theoretical investigations of the influence of the external noise on dynamics of a klystron oscillator

Experimental and theoretical investigations of the influence of an external noise source on a klystron oscillator with delayed feedback are performed. It is shown that the action of noise leads to suppression of regular, self-modulation, and chaotic signals of the klystron oscillator. The physical mechanism of generation suppression, which is related to the influence of noise on the value of the bunched beam current in the output klystron cavity is revealed. The possibility of the appearance of synchronization induced by noise in a klystron chaotic oscillator subjected to an external noise source is shown theoreticallyk.

Diagnostics of the Generalized Synchronization in Microwave Generators of Chaos

The generalized synchronization of chaos in a system of microwave generators based on klystron amplifiers with delayed feedback has been studied. A modification of the nearest neighbors method for diagnostics of generalized synchronization of chaos in systems with delayed feedback is developed. The efficiency of the modified method for processing experimental data is shown.

A Method for Determining the Transient Process Duration in Dynamic Systems in the Regime of Chaotic Oscillations

We describe a method for determining the transient process duration in a standard two-dimensional dynamic system with discrete time (Eno map), occurring in the regime of chaotic oscillations.

Specific features of generalized synchronization in unidirectionally and mutually coupled mappings and flows: Method of phase tubes

A concept of generalized synchronization in flow systems and discrete mappings is corrected and completed. It is rigorously demonstrated that the state vectors of interacting systems in the course of generalized synchronization must be considered as interrelated with the aid of a functional rather than a functional relation (as it is commonly accepted). An approach based on the analysis of the tubes of trajectories in phase space is proposed to determine the threshold of the generalized synchronization and study such type of synchronous behavior in the systems with discrete and continuous time. We conclude that the concept of weak and strong generalized synchronization must also be reconsidered.