Chaotic synchronization of coupled electron-wave systems with backward waves

The chaotic synchronization of two electron-wave media with interacting backward waves and cubic phase nonlinearity is investigated in the paper. To detect the chaotic synchronization regime we use a new approach, the so-called time scale synchronization [Chaos, 14 (3) 603-610 (2004)]. This approach is based on the consideration of the infinite set of chaotic signals' phases introduced by means of continuous wavelet transform. The complex space-time dynamics of the active media and mechanisms of the time scale synchronization appearance are considered.Comment: 11 pages, 7 figures, published in CHAOS, 15 (2005) 01370

Self-tuning of threshold for a two-state system

A two-state system (TSS) under time-periodic perturbations (to be regarded as input signals) is studied in connection with self-tuning (ST) of threshold and stochastic resonance (SR). By ST, we observe the improvement of signal-to-noise ratio (SNR) in a weak noise region. Analytic approach to a tuning equation reveals that SNR improvement is possible also for a large noise region and this is demonstrated by Monte Carlo simulations of hopping processes in a TSS. ST and SR are discussed from a little more physical point of energy transfer (dissipation) rate, which behaves in a similar way as SNR. Finally ST is considered briefly for a double-well potential system (DWPS), which is closely related to the TSS

Two Scenarios of Breaking Chaotic Phase Synchronization

Two types of phase synchronization (accordingly, two scenarios of breaking phase synchronization) between coupled stochastic oscillators are shown to exist depending on the discrepancy between the control parameters of interacting oscillators, as in the case of classical synchronization of periodic oscillators. If interacting stochastic oscillators are weakly detuned, the phase coherency of the attractors persists when phase synchronization breaks. Conversely, if the control parameters differ considerably, the chaotic attractor becomes phase-incoherent under the conditions of phase synchronization break.Comment: 8 pages, 7 figure

Synchronization of chaotic oscillator time scales

This paper deals with the chaotic oscillator synchronization. A new approach to detect the synchronized behaviour of chaotic oscillators has been proposed. This approach is based on the analysis of different time scales in the time series generated by the coupled chaotic oscillators. It has been shown that complete synchronization, phase synchronization, lag synchronization and generalized synchronization are the particular cases of the synchronized behavior called as "time--scale synchronization". The quantitative measure of chaotic oscillator synchronous behavior has been proposed. This approach has been applied for the coupled Rossler systems.Comment: 29 pages, 11 figures, published in JETP. 100, 4 (2005) 784-79

On the attractors of two-dimensional Rayleigh oscillators including noise

We study sustained oscillations in two-dimensional oscillator systems driven by Rayleigh-type negative friction. In particular we investigate the influence of mismatch of the two frequencies. Further we study the influence of external noise and nonlinearity of the conservative forces. Our consideration is restricted to the case that the driving is rather weak and that the forces show only weak deviations from radial symmetry. For this case we provide results for the attractors and the bifurcations of the system. We show that for rational relations of the frequencies the system develops several rotational excitations with right/left symmetry, corresponding to limit cycles in the four-dimensional phase space. The corresponding noisy distributions have the form of hoops or tires in the four-dimensional space. For irrational frequency relations, as well as for increasing strength of driving or noise the periodic excitations are replaced by chaotic oscillations.Comment: 9 pages, 5 figure