arXiv
(422,153 recursos)
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Mostrando recursos 121 - 140 de 13,166
121.
Synchronization of chaotic oscillator time scales - Hramov, Alexander E.; Koronovskii, Alexey A.; Levin, Yurij I.
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.
122.
Approximate Description of the Mandelbrot Set. Thermodynamic Analogy - Isaeva, O. B.; Kuznetsov, S. P.
Analogy between an approximate version of Feigenbaum renormalization group
analysis in complex domain and the phase transition theory of Yang-Lee (based
on consideration of formally complexified thermodynamic values) is discussed.
It is shown that the Julia sets of the renormalization transformation
correspond to the approximation of Mandelbrot set of the original map. New
aspects of analogy between the theory of dynamical systems and the phase
transition theory are uncovered.
123.
Projective Synchronization and Control of Unified Chaotic System - Feng, Liang; Jinglin, Xiang; Shaohua, Chen; Jie, Shi
The problem of projective synchronization(ps) and control are studied in
modified unified chaotic system which possess partially linearity property. The
desired ratio factor of corresponding subsystem variable could be obtained by
state feedback control. Theoretical analysis and numerical simulations are
provided to illustrate the projective synchronization and the feasibility of
the proposed control method. The effect on projective synchronization caused by
channel noise and parameter mismatch are investigated in detail, the results
showed that parameter mismatch has more effect on projective synchronization
than channel noise does, which may be applied to chaotic secure communications.
124.
Phase synchronization from noisy univariate signals - Rossberg, A. G.; Bartholome, K.; Voss, H. U.; Timmer, J.
We present methods for detecting phase synchronization of two
unidirectionally coupled, self-sustained noisy oscillators from a signal of the
driven oscillator alone. One method detects soft, another hard phase locking.
Both are applied to the problem of detecting phase synchronization in von
Karman vortex flow meters.
125.
Accumulation of embedded solitons in systems with quadratic nonlinearity - Malomed, B. A.; Wagenknecht, T.; Champneys, A. R.; Pearce, M. J.
Previous numerical studies have revealed the existence of embedded solitons
(ESs) in a class of multi-wave systems with quadratic nonlinearity, families of
which seem to emerge from a critical point in the parameter space, where the
zero solution has a fourfold zero eigenvalue. In this paper, the existence of
such solutions is studied in a three-wave model. An appropriate rescaling casts
the system in a normal form, which is universal for models supporting ESs
through quadratic nonlinearities. The normal-form system contains a single
irreducible parameter $\epsilon $, and is tantamount to the basic model of
type-I second-harmonic generation. An analytical approximation of WKB type
yields an asymptotic formula for...
126.
Pattern formation in parametric sound generation - Perez-Arjona, Isabel; Sanchez-Morcillo, Victor J.
Pattern formation of sound is predicted in a driven resonator where
subharmonic generation takes place. A model allowing for diffraction of the
fields (large-aspect ratio limit) is derived by means of the multiple scale
expansions technique. An analysis of the solutions and its stability against
space-dependent perturbations is performed in detail considering the
distinctive peculiarities of the acoustical system. Numerical integration
confirm the analytical predictions, and shows the possibility of patterns in
the form of stripes and squares.
127.
Post-critical set and non existence of preserved meromorphic two-forms - Bouamra, M.; Boukraa, S.; Hassani, S.; Maillard, J. -M.
We present a family of birational transformations in $ CP_2$ depending on
two, or three, parameters which does not, generically, preserve meromorphic
two-forms. With the introduction of the orbit of the critical set (vanishing
condition of the Jacobian), also called ``post-critical set'', we get some new
structures, some "non-analytic" two-form which reduce to meromorphic two-forms
for particular subvarieties in the parameter space. On these subvarieties, the
iterates of the critical set have a polynomial growth in the \emph{degrees of
the parameters}, while one has an exponential growth out of these subspaces.
The analysis of our birational transformation in $ CP_2$ is first carried out
using Diller-Favre criterion in order...
128.
B\"acklund transformations for fourth Painlev\'e hierarchies - Gordoa, Pilar R.; Joshi, Nalini; Pickering, Andrew
B\"acklund transformations (BTs) for ordinary differential equations (ODEs),
and in particular for hierarchies of ODEs, are a topic of great current
interest. Here we give an improved method of constructing BTs for hierarchies
of ODEs. This approach is then applied to fourth Painlev\'e ($P_{IV}$)
hierarchies recently found by the same authors [{\em Publ. Res. Inst. Math.
Sci. (Kyoto)} {\bf 37} 327--347 (2001)]. We show how the known pattern of BTs
for $P_{IV}$ can be extended to our $P_{IV}$ hierarchies. Remarkably, the BTs
required to do this are precisely the Miura maps of the dispersive water wave
hierarchy. We also obtain the important result that the fourth Painlev\'e
equation has...
129.
Synchrony of limit-cycle oscillators induced by random external impulses - Nakao, H.; Arai, K.; Nagai, K.; Tsubo, Y.; Kuramoto, Y.
The mechanism of phase synchronization between uncoupled limit-cycle
oscillators induced by common external impulsive forcing is analyzed. By
reducing the dynamics of the oscillator to a random phase map, it is shown that
phase synchronization generally occurs when the oscillator is driven by weak
external impulses in the limit of large inter-impulse intervals. The case where
the inter-impulse intervals are finite is also analyzed perturbatively for
small impulse intensity. For weak Poissonian impulses, it is shown that the
phase synchronization persists up to the first order approximation.
130.
Experimental study of two-dimensional enstrophy cascade - Boffetta, G.; Cenedese, A.; Espa, S.; Musacchio, S.
We study the direct enstrophy cascade in a two-dimensional flow generated in
an electromagnetically driven thin layer of fluid. Due to the presence of
bottom friction, the energy spectrum deviates from the classical Kraichnan
prediction $k^{-3}$. We find that the correction to the spectral slope depends
on the thickness on the layer, in agreement with a theoretical prediction based
on the analogy with passive scalar statistics.
131.
Independent Component Analysis of Spatiotemporal Chaos - Asano, H.; Nakao, H.
Two types of spatiotemporal chaos exhibited by ensembles of coupled nonlinear
oscillators are analyzed using independent component analysis (ICA). For
diffusively coupled complex Ginzburg-Landau oscillators that exhibit smooth
amplitude patterns, ICA extracts localized one-humped basis vectors that
reflect the characteristic hole structures of the system, and for nonlocally
coupled complex Ginzburg-Landau oscillators with fractal amplitude patterns,
ICA extracts localized basis vectors with characteristic gap structures.
Statistics of the decomposed signals also provide insight into the complex
dynamics of the spatiotemporal chaos.
132.
Poisson integrators - Karasözen, B.
An overview of Hamiltonian systems with noncanonical Poisson structures is
given. Examples of bi-Hamiltonian ode's, pde's and lattice equations are
presented. Numerical integrators using generating functions, Hamiltonian
splitting, symplectic Runge-Kutta methods are discussed for Lie-Poisson systems
and Hamiltonian systems with a general Poisson structure. Nambu-Poisson systems
and the discrete gradient methods are also presented.
133.
Generalized BBV Models for Weighted Complex Networks - Hu, Bo; Yan, Gang; Wang, Wen-Xu; Chen, Wen
We will introduce two evolving models that characterize weighted complex
networks. Though the microscopic dynamics are different, these models are found
to bear a similar mathematical framework, and hence exhibit some common
behaviors, for example, the power-law distributions and evolution of degree,
weight and strength. We also study the nontrivial clustering coefficient C and
tunable degree assortativity coefficient r, depending on specific parameters.
Most results are supported by present empirical evidences, and may provide us
with a better description of the hierarchies and organizational architecture of
weighted networks. Our models have been inspired by the weighted network model
proposed by Alain Barrat et al. (BBV for short), and can...
134.
Chaos synchronization in gap-junction-coupled neurons - Yoshioka, Masahiko
Depending on temperature the modified Hodgkin-Huxley (MHH) equations exhibit
a variety of dynamical behavior including intrinsic chaotic firing. We analyze
synchronization in a large ensemble of MHH neurons that are interconnected with
gap junctions. By evaluating tangential Lyapunov exponents we clarify whether
synchronous state of neurons is chaotic or periodic. Then, we evaluate
transversal Lyapunov exponents to elucidate if this synchronous state is stable
against infinitesimal perturbations. Our analysis elucidates that with weak gap
junctions, stability of synchronization of MHH neurons shows rather complicated
change with temperature. We, however, find that with strong gap junctions,
synchronous state is stable over the wide range of temperature irrespective of
whether synchronous state...
135.
On a transformation between hierarchies of integrable equations - Gurses, Metin; Zheltukhin, Kostyantyn
A transforation between a hierarchy of integrable equations arising from the
standard $R$-matrix construction on the algebra of differential operators and a
hierarchy of integrable equations arising from a deformation of the standard
$R$-matrix is given.
136.
Semiclassical transmission across transition states - Creagh, Stephen C.
It is shown that the probability of quantum-mechanical transmission across a
phase space bottleneck can be compactly approximated using an operator derived
from a complex Poincar\'e return map. This result uniformly incorporates
tunnelling effects with classically-allowed transmission and generalises a
result previously derived for a classically small region of phase space.
137.
Uniform approximation of barrier penetration in phase space - Drew, Christopher S.; Creagh, Stephen C.; Tew, Richard H.
A method to approximate transmission probabilities for a nonseparable
multidimensional barrier is applied to a waveguide model. The method uses
complex barrier-crossing orbits to represent reaction probabilities in phase
space and is uniform in the sense that it applies at and above a threshold
energy at which classical reaction switches on. Above this threshold the
geometry of the classically reacting region of phase space is clearly reflected
in the quantum representation. Two versions of the approximation are applied. A
harmonic version which uses dynamics linearised around an instanton orbit is
valid only near threshold but is easy to use. A more accurate and more widely
applicable version using nonlinear...
138.
Optimal phase space projection for noise reduction - Luo, Xiaodong; Zhang, Jie; Small, Michael
In this communication we will re-examine the widely studied technique of
phase space projection. By imposing a time domain constraint (TDC) on the
residual noise, we deduce a more general version of the optimal projector,
which includes those appearing in previous literature as subcases but does not
assume the independence between the clean signal and the noise. As an
application, we will apply this technique for noise reduction. Numerical
results show that our algorithm has succeeded in augmenting the signal-to-noise
ratio (SNR) for simulated data from the R\"ossler system and experimental
speech record.
139.
Synchronization and clustering in electroencephalographic signals - Escalona-Moran, M.; Cosenza, M. G.; Guillen, P.; Coutin, P.
The degree of synchronization and the amount of dynamical cluster formation
in electroencephalographic (EEG) signals are characterized by employing two
order parameters introduced in the context of coupled chaotic systems subject
to external noise. These parameters are calculated in EEG signals from a group
of healthy subjects and a group of epileptic patients, including a patient
experiencing an epileptic crisis. The evolution of these parameters shows the
occurrence of intermittent synchronization and clustering in the brain activity
during an epileptic crisis. Significantly, the existence of an instantaneous
maximum of synchronization previous to the onset of a crisis is revealed by
this procedure. The mean values of the order parameters...
140.
Energy localization in two chaotically coupled systems - Gronqvist, Johan; Guhr, Thomas
We set up and analyze a random matrix model to study energy localization and
its time behavior in two chaotically coupled systems. This investigation is
prompted by a recent experimental and theoretical study of Weaver and Lobkis on
coupled elastomechanical systems. Our random matrix model properly describes
the main features of the findings by Weaver and Lobkis. Due to its general
character, our model is also applicable to similar systems in other areas of
physics -- for example, to chaotically coupled quantum dots.
121.
