381 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
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
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.
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
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
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
The impact of climate change on countries’ interdependence on genetic resources for food and agriculture: An executive summary
The System-wide Genetic Resources Programme (SGRP) of the CGIAR coordinated the development of a background study paper entitled ‘The Impact of Climate Change on Countries Interdependence on Genetic Resources for Food and Agriculture’ for the Twelfth Session of the FAO Commission on Genetic Resources for Food and Agriculture. The purpose of the paper was to contribute to the Commission’s consideration of policies and arrangements for access and benefit-sharing for genetic resources for food and agriculture. This document is an executive summary of that paper
Universal Scaling Properties in Large Assemblies of Simple Dynamical Units Driven by Long-Wave Random Forcing
Large assemblies of nonlinear dynamical units driven by a long-wave
fluctuating external field are found to generate strong turbulence with scaling
properties. This type of turbulence is so robust that it persists over a finite
parameter range with parameter-dependent exponents of singularity, and is
insensitive to the specific nature of the dynamical units involved. Whether or
not the units are coupled with their neighborhood is also unimportant. It is
discovered numerically that the derivative of the field exhibits strong spatial
intermittency with multifractal structure.Comment: 10 pages, 7 figures, submitted to PR
Statistics of finite-time Lyapunov exponents in the Ulam map
The statistical properties of finite-time Lyapunov exponents at the Ulam
point of the logistic map are investigated. The exact analytical expression for
the autocorrelation function of one-step Lyapunov exponents is obtained,
allowing the calculation of the variance of exponents computed over time
intervals of length . The variance anomalously decays as . The
probability density of finite-time exponents noticeably deviates from the
Gaussian shape, decaying with exponential tails and presenting spikes
that narrow and accumulate close to the mean value with increasing . The
asymptotic expression for this probability distribution function is derived. It
provides an adequate smooth approximation to describe numerical histograms
built for not too small , where the finiteness of bin size trimmes the sharp
peaks.Comment: 6 pages, 4 figures, to appear in Phys. Rev.
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