386 research outputs found
Analysis of chaotic motion and its shape dependence in a generalized piecewise linear map
We analyse the chaotic motion and its shape dependence in a piecewise linear
map using Fujisaka's characteristic function method. The map is a
generalization of the one introduced by R. Artuso. Exact expressions for
diffusion coefficient are obtained giving previously obtained results as
special cases. Fluctuation spectrum relating to probability density function is
obtained in a parametric form. We also give limiting forms of the above
quantities. Dependence of diffusion coefficient and probability density
function on the shape of the map is examined.Comment: 4 pages,4 figure
Continued-fraction expansion of eigenvalues of generalized evolution operators in terms of periodic orbits
A new expansion scheme to evaluate the eigenvalues of the generalized
evolution operator (Frobenius-Perron operator) relevant to the
fluctuation spectrum and poles of the order- power spectrum is proposed. The
``partition function'' is computed in terms of unstable periodic orbits and
then used in a finite pole approximation of the continued fraction expansion
for the evolution operator. A solvable example is presented and the approximate
and exact results are compared; good agreement is found.Comment: CYCLER Paper 93mar00
Synchronization of Coupled Systems with Spatiotemporal Chaos
We argue that the synchronization transition of stochastically coupled
cellular automata, discovered recently by L.G. Morelli {\it et al.} (Phys. Rev.
{\bf 58 E}, R8 (1998)), is generically in the directed percolation universality
class. In particular, this holds numerically for the specific example studied
by these authors, in contrast to their claim. For real-valued systems with
spatiotemporal chaos such as coupled map lattices, we claim that the
synchronization transition is generically in the universality class of the
Kardar-Parisi-Zhang equation with a nonlinear growth limiting term.Comment: 4 pages, including 3 figures; submitted to Phys. Rev.
Phase synchronization in time-delay systems
Though the notion of phase synchronization has been well studied in chaotic
dynamical systems without delay, it has not been realized yet in chaotic
time-delay systems exhibiting non-phase coherent hyperchaotic attractors. In
this article we report the first identification of phase synchronization in
coupled time-delay systems exhibiting hyperchaotic attractor. We show that
there is a transition from non-synchronized behavior to phase and then to
generalized synchronization as a function of coupling strength. These
transitions are characterized by recurrence quantification analysis, by phase
differences based on a new transformation of the attractors and also by the
changes in the Lyapunov exponents. We have found these transitions in coupled
piece-wise linear and in Mackey-Glass time-delay systems.Comment: 4 pages, 3 Figures (To appear in Physical Review E Rapid
Communication
Critical exponents in zero dimensions
In the vicinity of the onset of an instability, we investigate the effect of
colored multiplicative noise on the scaling of the moments of the unstable mode
amplitude. We introduce a family of zero dimensional models for which we can
calculate the exact value of the critical exponents for all the
moments. The results are obtained through asymptotic expansions that use the
distance to onset as a small parameter. The examined family displays a variety
of behaviors of the critical exponents that includes anomalous exponents:
exponents that differ from the deterministic (mean-field) prediction, and
multiscaling: non-linear dependence of the exponents on the order of the
moment
Fundamental scaling laws of on-off intermittency in a stochastically driven dissipative pattern forming system
Noise driven electroconvection in sandwich cells of nematic liquid crystals
exhibits on-off intermittent behaviour at the onset of the instability. We
study laser scattering of convection rolls to characterize the wavelengths and
the trajectories of the stochastic amplitudes of the intermittent structures.
The pattern wavelengths and the statistics of these trajectories are in
quantitative agreement with simulations of the linearized electrohydrodynamic
equations. The fundamental distribution law for the durations
of laminar phases as well as the power law of the amplitude distribution
of intermittent bursts are confirmed in the experiments. Power spectral
densities of the experimental and numerically simulated trajectories are
discussed.Comment: 20 pages and 17 figure
Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators
We show that a wide class of uncoupled limit cycle oscillators can be
in-phase synchronized by common weak additive noise. An expression of the
Lyapunov exponent is analytically derived to study the stability of the
noise-driven synchronizing state. The result shows that such a synchronization
can be achieved in a broad class of oscillators with little constraint on their
intrinsic property. On the other hand, the leaky integrate-and-fire neuron
oscillators do not belong to this class, generating intermittent phase slips
according to a power low distribution of their intervals.Comment: 10 pages, 3 figure
Slower Speed and Stronger Coupling: Adaptive Mechanisms of Self-Organized Chaos Synchronization
We show that two initially weakly coupled chaotic systems can achieve
self-organized synchronization by adaptively reducing their speed and/or
enhancing the coupling strength. Explicit adaptive algorithms for
speed-reduction and coupling-enhancement are provided. We apply these
algorithms to the self-organized synchronization of two coupled Lorenz systems.
It is found that after a long-time self-organized process, the two coupled
chaotic systems can achieve synchronization with almost minimum required
coupling-speed ratio.Comment: 4 pages, 5 figure
An Interference Cancellation Scheme for TFI-OFDM in Time-Variant Large Delay Spread Channel
In the mobile radio environment, signals are usually impaired by fading and multipath delay phenomenon. In such channels, severe fading of the signal amplitude and inter-symbol-interference (ISI) due to the frequency selectivity of the channel cause an unacceptable degradation of error performance. Orthogonal frequency division multiplexing (OFDM) is an efficient scheme to mitigate the effect of multipath channel. Since it eliminates ISI by inserting guard interval (GI) longer than the delay spread of the channel. In general, the GI is usually designed to be longer than the delay spread of the channel, and is decided after channel measurements in the desired implementation scenario. However, the maximum delay spread is longer than GI, the system performance is significantly degraded. The conventional time-frequency interferometry (TFI) for OFDM does not consider timevariant channel with large delay spread. In this paper, we focus on the large delay spread channel and propose the ISI and inter-carrier-interference (ICI) compensation method for TFI-OFDM
Non-Markovian Levy diffusion in nonhomogeneous media
We study the diffusion equation with a position-dependent, power-law
diffusion coefficient. The equation possesses the Riesz-Weyl fractional
operator and includes a memory kernel. It is solved in the diffusion limit of
small wave numbers. Two kernels are considered in detail: the exponential
kernel, for which the problem resolves itself to the telegrapher's equation,
and the power-law one. The resulting distributions have the form of the L\'evy
process for any kernel. The renormalized fractional moment is introduced to
compare different cases with respect to the diffusion properties of the system.Comment: 7 pages, 2 figure
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