27,416 research outputs found
Fractional Fourier detection of L\'evy Flights: application to Hamiltonian chaotic trajectories
A signal processing method designed for the detection of linear (coherent)
behaviors among random fluctuations is presented. It is dedicated to the study
of data recorded from nonlinear physical systems. More precisely the method is
suited for signals having chaotic variations and sporadically appearing regular
linear patterns, possibly impaired by noise. We use time-frequency techniques
and the Fractional Fourier transform in order to make it robust and easily
implementable. The method is illustrated with an example of application: the
analysis of chaotic trajectories of advected passive particles. The signal has
a chaotic behavior and encounter L\'evy flights (straight lines). The method is
able to detect and quantify these ballistic transport regions, even in noisy
situations
Time-frequency analysis of the restricted three-body problem: transport and resonance transitions
A method of time-frequency analysis based on wavelets is applied to the problem of transport between different regions of the solar system, using the model of the circular restricted three-body problem in both the planar and the spatial versions of the problem.. The method is based on the extraction of instantaneous frequencies from the wavelet transform of numerical solutions. Time-varying frequencies provide a good diagnostic tool to discern chaotic trajectories from regular ones, and we can identify resonance islands that greatly affect the dynamics. Good accuracy in the calculation of time-varying frequencies allows us to determine resonance trappings of chaotic trajectories and resonance transitions. We show the relation between resonance transitions and transport in different regions of the phase space
Comprehensive experimental analysis of nonlinear dynamics in an optically-injected semiconductor laser
We present the first comprehensive experimental study, to our knowledge, of the routes between nonlinear dynamics induced in a semiconductor laser under external optical injection based on an analysis of time-averaged measurements of the optical and RF spectra and phasors of real-time series of the laser output. The different means of analysis are compared for several types of routes and the benefits of each are discussed in terms of the identification and mapping of the nonlinear dynamics. Finally, the results are presented in a novel audio/video format that describes the evolution of the dynamics with the injection parameters. © 2011 Author(s)
Frequency and Phase Synchronization in Neuromagnetic Cortical Responses to Flickering-Color Stimuli
In our earlier study dealing with the analysis of neuromagnetic responses
(magnetoencephalograms - MEG) to flickering-color stimuli for a group of
control human subjects (9 volunteers) and a patient with photosensitive
epilepsy (a 12-year old girl), it was shown that Flicker-Noise Spectroscopy
(FNS) was able to identify specific differences in the responses of each
organism. The high specificity of individual MEG responses manifested itself in
the values of FNS parameters for both chaotic and resonant components of the
original signal. The present study applies the FNS cross-correlation function
to the analysis of correlations between the MEG responses simultaneously
measured at spatially separated points of the human cortex processing the
red-blue flickering color stimulus. It is shown that the cross-correlations for
control (healthy) subjects are characterized by frequency and phase
synchronization at different points of the cortex, with the dynamics of
neuromagnetic responses being determined by the low-frequency processes that
correspond to normal physiological rhythms. But for the patient, the frequency
and phase synchronization breaks down, which is associated with the suppression
of cortical regulatory functions when the flickering-color stimulus is applied,
and higher frequencies start playing the dominating role. This suggests that
the disruption of correlations in the MEG responses is the indicator of
pathological changes leading to photosensitive epilepsy, which can be used for
developing a method of diagnosing the disease based on the analysis with the
FNS cross-correlation function.Comment: 21 pages, 14 figures; submitted to "Laser Physics", 2010, 2
Observation of chaotic beats in a driven memristive Chua's circuit
In this paper, a time varying resistive circuit realising the action of an
active three segment piecewise linear flux controlled memristor is proposed.
Using this as the nonlinearity, a driven Chua's circuit is implemented. The
phenomenon of chaotic beats in this circuit is observed for a suitable choice
of parameters. The memristor acts as a chaotically time varying resistor
(CTVR), switching between a less conductive OFF state and a more conductive ON
state. This chaotic switching is governed by the dynamics of the driven Chua's
circuit of which the memristor is an integral part. The occurrence of beats is
essentially due to the interaction of the memristor aided self oscillations of
the circuit and the external driving sinusoidal forcing. Upon slight
tuning/detuning of the frequencies of the memristor switching and that of the
external force, constructive and destructive interferences occur leading to
revivals and collapses in amplitudes of the circuit variables, which we refer
as chaotic beats. Numerical simulations and Multisim modelling as well as
statistical analyses have been carried out to observe as well as to understand
and verify the mechanism leading to chaotic beats.Comment: 30 pages, 16 figures; Submitted to IJB
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
3D billiards: visualization of regular structures and trapping of chaotic trajectories
The dynamics in three-dimensional billiards leads, using a Poincar\'e
section, to a four-dimensional map which is challenging to visualize. By means
of the recently introduced 3D phase-space slices an intuitive representation of
the organization of the mixed phase space with regular and chaotic dynamics is
obtained. Of particular interest for applications are constraints to classical
transport between different regions of phase space which manifest in the
statistics of Poincar\'e recurrence times. For a 3D paraboloid billiard we
observe a slow power-law decay caused by long-trapped trajectories which we
analyze in phase space and in frequency space. Consistent with previous results
for 4D maps we find that: (i) Trapping takes place close to regular structures
outside the Arnold web. (ii) Trapping is not due to a generalized
island-around-island hierarchy. (iii) The dynamics of sticky orbits is governed
by resonance channels which extend far into the chaotic sea. We find clear
signatures of partial transport barriers. Moreover, we visualize the geometry
of stochastic layers in resonance channels explored by sticky orbits.Comment: 20 pages, 11 figures. For videos of 3D phase-space slices and
time-resolved animations see http://www.comp-phys.tu-dresden.de/supp
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