155 research outputs found
Superdiffusion in the Dissipative Standard Map
We consider transport properties of the chaotic (strange) attractor along
unfolded trajectories of the dissipative standard map. It is shown that the
diffusion process is normal except of the cases when a control parameter is
close to some special values that correspond to the ballistic mode dynamics.
Diffusion near the related crisises is anomalous and non-uniform in time: there
are large time intervals during which the transport is normal or ballistic, or
even superballistic. The anomalous superdiffusion seems to be caused by
stickiness of trajectories to a non-chaotic and nowhere dense invariant Cantor
set that plays a similar role as cantori in Hamiltonian chaos. We provide a
numerical example of such a sticky set. Distribution function on the sticky set
almost coincides with the distribution function (SRB measure) of the chaotic
attractor.Comment: 10 Figure
Chaotic Observer-based Synchronization Under Information Constraints
Limit possibilities of observer-based synchronization systems under
information constraints (limited information capacity of the coupling channel)
are evaluated. We give theoretical analysis for multi-dimensional
drive-response systems represented in the Lurie form (linear part plus
nonlinearity depending only on measurable outputs). It is shown that the upper
bound of the limit synchronization error (LSE) is proportional to the upper
bound of the transmission error. As a consequence, the upper and lower bounds
of LSE are proportional to the maximum rate of the coupling signal and
inversely proportional to the information transmission rate (channel capacity).
Optimality of the binary coding for coders with one-step memory is established.
The results are applied to synchronization of two chaotic Chua systems coupled
via a channel with limited capacity.Comment: 7 pages, 6 figures, 27 reference
Effect of periodic parametric excitation on an ensemble of force-coupled self-oscillators
We report the synchronization behavior in a one-dimensional chain of
identical limit cycle oscillators coupled to a mass-spring load via a force
relation. We consider the effect of periodic parametric modulation on the final
synchronization states of the system. Two types of external parametric
excitations are investigated numerically: periodic modulation of the stiffness
of the inertial oscillator and periodic excitation of the frequency of the
self-oscillatory element. We show that the synchronization scenarios are ruled
not only by the choice of parameters of the excitation force but depend on the
initial collective state in the ensemble. We give detailed analysis of
entrainment behavior for initially homogeneous and inhomogeneous states. Among
other results, we describe a regime of partial synchronization. This regime is
characterized by the frequency of collective oscillation being entrained to the
stimulation frequency but different from the average individual oscillators
frequency.Comment: Comments and suggestions are welcom
Behavior of the Escape Rate Function in Hyperbolic Dynamical Systems
For a fixed initial reference measure, we study the dependence of the escape
rate on the hole for a smooth or piecewise smooth hyperbolic map. First, we
prove the existence and Holder continuity of the escape rate for systems with
small holes admitting Young towers. Then we consider general holes for Anosov
diffeomorphisms, without size or Markovian restrictions. We prove bounds on the
upper and lower escape rates using the notion of pressure on the survivor set
and show that a variational principle holds under generic conditions. However,
we also show that the escape rate function forms a devil's staircase with jumps
along sequences of regular holes and present examples to elucidate some of the
difficulties involved in formulating a general theory.Comment: 21 pages. v2 differs from v1 only by additions to the acknowledgment
The MHD nature of ionospheric wave packets excited by the solar terminator
We obtained the first experimental evidence for the magnetohydrodynamic (MHD)
nature of ionospheric medium-scale travelling wave packets (MSTWP). We used
data on total electron content (TEC) measurements obtained at the dense
Japanese network GPS/GEONET (1220 stations) in 2008-2009. We found that the
diurnal, seasonal and spectral MSTWP characteristics are specified by the solar
terminator (ST) dynamics. MSTWPs are the chains of narrow-band TEC oscillations
with single packet's duration of about 1-2 hours and oscillation periods of
10-20 minutes. Their total duration is about 4--6 hours. The MSTWP spatial
structure is characterized by a high degree of anisotropy and coherence at the
distance of more than 10 wavelengths. The MSTWP direction of travelling is
characterized by a high directivity regardless of seasons. Occurrence rate of
daytime MSTWPs is high in winter and during equinoxes. Occurrence rate of
nighttime MSTIDs has its peak in summer. These features are consistent with
previous MS travelling ionosphere disturbance (TID) statistics obtained from
630-nm airglow imaging observations in Japan. In winter, MSTWPs in the northern
hemisphere are observed 3-4 hours after the morning ST passage. In summer,
MSTWPs are detected 1.5-2 hours before the evening ST occurrence at the point
of observations, at the moment of the evening ST passage in the
magneto-conjugate point. Both the high Q-factor of oscillatory system and
synchronization of MSTWP occurrence with the solar terminator passage at the
point of observations and in the magneto-conjugate area testify the MHD nature
of ST-excited MSTWP generation. The obtained results are the first experimental
evidence for the hypothesis of the ST-generated ion sound waves.Comment: 12 pages, 3 figure
Synchronous Behavior of Two Coupled Electronic Neurons
We report on experimental studies of synchronization phenomena in a pair of
analog electronic neurons (ENs). The ENs were designed to reproduce the
observed membrane voltage oscillations of isolated biological neurons from the
stomatogastric ganglion of the California spiny lobster Panulirus interruptus.
The ENs are simple analog circuits which integrate four dimensional
differential equations representing fast and slow subcellular mechanisms that
produce the characteristic regular/chaotic spiking-bursting behavior of these
cells. In this paper we study their dynamical behavior as we couple them in the
same configurations as we have done for their counterpart biological neurons.
The interconnections we use for these neural oscillators are both direct
electrical connections and excitatory and inhibitory chemical connections: each
realized by analog circuitry and suggested by biological examples. We provide
here quantitative evidence that the ENs and the biological neurons behave
similarly when coupled in the same manner. They each display well defined
bifurcations in their mutual synchronization and regularization. We report
briefly on an experiment on coupled biological neurons and four dimensional ENs
which provides further ground for testing the validity of our numerical and
electronic models of individual neural behavior. Our experiments as a whole
present interesting new examples of regularization and synchronization in
coupled nonlinear oscillators.Comment: 26 pages, 10 figure
Asymptotically stable phase synchronization revealed by autoregressive circle maps
A new type of nonlinear time series analysis is introduced, based on phases,
which are defined as polar angles in spaces spanned by a finite number of
delayed coordinates. A canonical choice of the polar axis and a related
implicit estimation scheme for the potentially underlying auto-regressive
circle map (next phase map) guarantee the invertibility of reconstructed phase
space trajectories to the original coordinates. The resulting Fourier
approximated, Invertibility enforcing Phase Space map (FIPS map) is well suited
to detect conditional asymptotic stability of coupled phases. This rather
general synchronization criterion unites two existing generalisations of the
old concept and can successfully be applied e.g. to phases obtained from ECG
and airflow recordings characterizing cardio-respiratory interaction.Comment: PDF file, 232 KB, 24 pages, 3 figures; cheduled for Phys. Rev. E
(Nov) 200
Delayed Self-Synchronization in Homoclinic Chaos
The chaotic spike train of a homoclinic dynamical system is self-synchronized
by re-inserting a small fraction of the delayed output. Due to the sensitive
nature of the homoclinic chaos to external perturbations, stabilization of very
long periodic orbits is possible. On these orbits, the dynamics appears chaotic
over a finite time, but then it repeats with a recurrence time that is slightly
longer than the delay time. The effect, called delayed self-synchronization
(DSS), displays analogies with neurodynamic events which occur in the build-up
of long term memories.Comment: Submitted to Phys. Rev. Lett., 13 pages, 7 figure
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