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

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

Effective Fokker-Planck Equation for Birhythmic Modified van der Pol Oscillator

We present an explicit solution based on the phase-amplitude approximation of the Fokker-Planck equation associated with the Langevin equation of the birhythmic modified van der Pol system. The solution enables us to derive probability distributions analytically as well as the activation energies associated to switching between the coexisting different attractors that characterize the birhythmic system. Comparing analytical and numerical results we find good agreement when the frequencies of both attractors are equal, while the predictions of the analytic estimates deteriorate when the two frequencies depart. Under the effect of noise the two states that characterize the birhythmic system can merge, inasmuch as the parameter plane of the birhythmic solutions is found to shrink when the noise intensity increases. The solution of the Fokker-Planck equation shows that in the birhythmic region, the two attractors are characterized by very different probabilities of finding the system in such a state. The probability becomes comparable only for a narrow range of the control parameters, thus the two limit cycles have properties in close analogy with the thermodynamic phases

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

Time scale synchronization of chaotic oscillators

This paper presents the result of the investigation of chaotic oscillator synchronization. A new approach for detecting of 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. This approach has been applied for the coupled Rossler and Lorenz systems.Comment: 19 pages, 12 figure

The role of noise in forming the dynamics of a quasiperiodic system

The dynamical properties of the quasiperiodic logistic map with and without a very weak noise are compared, and the influence of noise on its strange nonchaotic attractor (SNA) is investigated. It is found that, in the presence of weak noise, the largest Lyapunov exponent gives misleading information about the dynamical properties of the attractor. We have shown that, in the presence of noise, the properties of strangeness and chaos are invariably associated, so that SNAs are not then observed during the transition to chaos from the torus