295 research outputs found
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
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
Synthesis of adaptive critical control methods, identification and management
The main problem of dynamic plant control is the variability of the parameters of the control object, and we are talking even about the nature of external disturbances, the lack of information about their statistical or stochastic characteristics. An approach to the development of an adaptive controller based on the recurrent least squares method is proposed
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
Noise induced escape from different types of chaotic attractor
Noise-induced escape from a quasi-attractor, and from the Lorenz attractor with non-fractal boundaries, are compared through measurements of optimal paths. It has been found that, for both types of attractor, there exists a most probable (optimal) escape trajectory, the prehistory of the escape being defined by the structure of the chaotic attractor. For a quasi-attractor the escape process is realized via several steps, which include transitions between low-period saddle cycles co-existing in the system phase space. The prehistory of escape from the Lorenz attractor is defined by stable and unstable manifolds of the saddle center point, and the escape itself consists of crossing the saddle cycle surrounding one of the stable point-attractors
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
Detecting synchronization of self-sustained oscillators by external driving with varying frequency
We propose a method for detecting the presence of synchronization of
self-sustained oscillator by external driving with linearly varying frequency.
The method is based on a continuous wavelet transform of the signals of
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 driven van der Pol
oscillator and to experimental data of human heart rate variability and
respiration.Comment: 9 pages, 7 figure
Global stability analysis of birhythmicity in a self-sustained oscillator
We analyze global stability properties of birhythmicity in a self-sustained
system with random excitations. The model is a multi-limit cycles variation of
the van der Pol oscillatorintroduced to analyze enzymatic substrate reactions
in brain waves. We show that the two frequencies are strongly influenced by the
nonlinear coefficients and . With a random excitation, such as
a Gaussian white noise, the attractor's global stability is measured by the
mean escape time from one limit-cycle. An effective activation energy
barrier is obtained by the slope of the linear part of the variation of the
escape time versus the inverse noise-intensity 1/D. We find that the
trapping barriers of the two frequencies can be very different, thus leaving
the system on the same attractor for an overwhelming time. However, we also
find that the system is nearly symmetric in a narrow range of the parameters.Comment: 17 pages, 8 figures, to appear on Choas, 201
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