Alexey A. Koronovskii

Generalized synchronization of chaos for secure communication: Remarkable stability to noise

A new method for secure information transmission based on generalized synchronization is proposed. The principal advantage of it is a remarkable stability to noise. To reveal this peculiarity of the proposed method the effectiveness of the detection of the information signal from the transmitted one in the presence of noise in the communication channel is examined both for the proposed scheme and for the schemes of chaotic communication known already. The main ideas of the proposed method are illustrated by the example of coupled Rossler systems used both transmitter and receiver.

Wavelets in Neuroscience

MathematicalMethods of Signal Processing in Neuroscience.- Brief Tour of Wavelet Theory.- Analysis of Single Neuron Recordings.- Classification of Neuronal Spikes from Extracellular Recordings.- Wavelet Approach to the Study of Rhythmic Neuronal Activity.- Time-Frequency Analysis of EEG: From Theory to Practice.- Automatic Diagnostics and Processing of EEG.- Conclusion.- Index.

First experimental observation of generalized synchronization phenomena in microwave oscillators.

In this Letter, we report for the first time on the experimental observation of the generalized synchronization regime in the microwave electronic systems, namely, in the multicavity klystron generators. A new approach devoted to the generalized synchronization detection has been developed. The experimental observations are in the excellent agreement with the results of numerical simulation. The observed phenomena gives a strong potential for new applications requiring microwave chaotic signals.

On-off intermittency in time series of spontaneous paroxysmal activity in rats with genetic absence epilepsy

In the present paper we consider the on-off intermittency phenomena observed in time series of spontaneous paroxysmal activity in rats with genetic absence epilepsy. The method to register and analyze the electroencephalogram with the help of continuous wavelet transform is also suggested.

Chaotic synchronization in coupled spatially extended beam-plasma systems

Abstract The appearance of the chaotic synchronization regimes has been discovered for the coupled spatially extended beam–plasma Pierce systems. The coupling was introduced only on the right bound of each subsystem. It has been shown that with coupling increase the spatially extended beam–plasma systems show the transition from asynchronous behavior to the phase synchronization and then to the complete synchronization regime. For the consideration of the chaotic synchronization we used the concept of time-scale synchronization described in work [A.E. Hramov, A.A. Koronovskii, Chaos 14 (3) (2004) 603] and based on the introduction of the continuous set of phases of chaotic signal. In case of unidirectional coupling the generalized synchronization regime has been observed in the spatially extended beam–plasma systems. The generalized synchronization appearance mechanism has been analyzed by means of the offered modified system approach [A.E. Hramov, A.A. Koronovskii, Phys. Rev. E 71 (6) (2005) 067201].

Effect of temperature on resonant electron transport through stochastic conduction channels in superlattices

We show that resonant electron transport in semiconductor superlattices with an applied electric and tilted magnetic field can, surprisingly, become more pronounced as the lattice and conduction electron temperature increases from 4.2 K to room temperature and beyond. It has previously been demonstrated that at certain critical field parameters, the semiclassical trajectories of electrons in the lowest miniband of the superlattice change abruptly from fully localized to completely unbounded. The unbounded electron orbits propagate through intricate web patterns, known as stochastic webs, in phase space, which act as conduction channels for the electrons and produce a series of resonant peaks in the electron drift velocity versus electric-field curves. Here, we show that increasing the lattice temperature strengthens these resonant peaks due to a subtle interplay between the thermal population of the conduction channels and transport along them. This enhances both the electron drift velocity and the influence of the stochastic webs on the current-voltage characteristics, which we calculate by making self-consistent solutions of the coupled electron transport and Poisson equations throughout the superlattice. These solutions reveal that increasing the temperature also transforms the collective electron dynamics by changing both the threshold voltage required for the onset of self-sustained current oscillations, produced by propagating charge domains, and the oscillation frequency.

Detecting synchronization of self-sustained oscillators by external driving with varying frequency

We propose a method for detecting the presence of a synchronization of a self-sustained oscillator by external driving with linearly varying frequency. The method is based on a continuous wavelet transform of the signals of the self-sustained oscillator and external force and allows one to distinguish the case of true synchronization from the case of spurious synchronization caused by linear mixing of the signals. We apply the method to a driven van der Pol oscillator and to experimental data of human heart rate variability and respiration.

Generalized synchronization in mutually coupled oscillators and complex networks.

We introduce a concept of generalized synchronization, able to encompass the setting of collective synchronized behavior for mutually coupled systems and networking systems featuring complex topologies in their connections. The onset of the synchronous regime is confirmed by the dependence of the systems Lyapunov exponents on the coupling parameter. The presence of a generalized synchronization regime is verified by means of the nearest neighbor method.

Microwave radiation power of relativistic electron beam with virtual cathode in the external magnetic field

The study of the output power of the electromagnetic radiation of the relativistic electron beam (REB) with virtual cathode in the presence of external magnetic field has been found out. The typical dependencies of the output microwave power of the vircator versus external magnetic field have been analyzed by means of 3D electromagnetic simulation. It has been shown that the power of vircator demonstrates several maxima with external magnetic field growth. The characteristic features of the power behavior are determined by the conditions of the virtual cathode formation in the presence of the external transversal magnetic field and the REB self-magnetic fields.

Computation of the spectrum of spatial Lyapunov exponents for the spatially extended beam-plasma systems and electron-wave devices

The spectrum of Lyapunov exponents is powerful tool for the analysis of the complex system dynamics. In the general framework of nonlinear dynamics, a number of the numerical techniques have been developed to obtain the spectrum of Lyapunov exponents for the complex temporal behavior of the systems with a few degree of freedom. Unfortunately, these methods cannot be applied directly to analysis of complex spatio-temporal dynamics of plasma devices which are characterized by the infinite phase space, since they are the spatially extended active media. In the present paper, we propose the method for the calculation of the spectrum of the spatial Lyapunov exponents (SLEs) for the spatially extended beam-plasma systems. The calculation technique is applied to the analysis of chaotic spatio-temporal oscillations in three different beam-plasma model: (1) simple plasma Pierce diode, (2) coupled Pierce diodes, and (3) electron-wave system with backward electromagnetic wave. We find an excellent agreement between ...