335 research outputs found
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
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