1,842 research outputs found
Notes on Exact Multi-Soliton Solutions of Noncommutative Integrable Hierarchies
We study exact multi-soliton solutions of integrable hierarchies on
noncommutative space-times which are represented in terms of quasi-determinants
of Wronski matrices by Etingof, Gelfand and Retakh. We analyze the asymptotic
behavior of the multi-soliton solutions and found that the asymptotic
configurations in soliton scattering process can be all the same as commutative
ones, that is, the configuration of N-soliton solution has N isolated localized
energy densities and the each solitary wave-packet preserves its shape and
velocity in the scattering process. The phase shifts are also the same as
commutative ones. Furthermore noncommutative toroidal Gelfand-Dickey hierarchy
is introduced and the exact multi-soliton solutions are given.Comment: 18 pages, v3: references added, version to appear in JHE
Emergence of chaotic behaviour in linearly stable systems
Strong nonlinear effects combined with diffusive coupling may give rise to
unpredictable evolution in spatially extended deterministic dynamical systems
even in the presence of a fully negative spectrum of Lyapunov exponents. This
regime, denoted as ``stable chaos'', has been so far mainly characterized by
numerical studies. In this manuscript we investigate the mechanisms that are at
the basis of this form of unpredictable evolution generated by a nonlinear
information flow through the boundaries. In order to clarify how linear
stability can coexist with nonlinear instability, we construct a suitable
stochastic model. In the absence of spatial coupling, the model does not reveal
the existence of any self-sustained chaotic phase. Nevertheless, already this
simple regime reveals peculiar differences between the behaviour of finite-size
and that of infinitesimal perturbations. A mean-field analysis of the truly
spatially extended case clarifies that the onset of chaotic behaviour can be
traced back to the diffusion process that tends to shift the growth rate of
finite perturbations from the quenched to the annealed average. The possible
characterization of the transition as the onset of directed percolation is also
briefly discussed as well as the connections with a synchronization transition.Comment: 30 pages, 8 figures, Submitted to Journal of Physics
Zero delay synchronization of chaos in coupled map lattices
We show that two coupled map lattices that are mutually coupled to one
another with a delay can display zero delay synchronization if they are driven
by a third coupled map lattice. We analytically estimate the parametric regimes
that lead to synchronization and show that the presence of mutual delays
enhances synchronization to some extent. The zero delay or isochronal
synchronization is reasonably robust against mismatches in the internal
parameters of the coupled map lattices and we analytically estimate the
synchronization error bounds.Comment: 9 pages, 9 figures ; To appear in Phys. Rev.
Replicated INAR(1) processes
Replicated time series are a particular type of repeated measures, which consist of time-sequences of measurements taken from several subjects (experimental units). We consider independent replications of count time series that are modelled by first-order integer-valued autoregressive processes, INAR(1). In this work, we propose several estimation methods using the classical and the Bayesian approaches and both in time and frequency domains. Furthermore, we study the asymptotic properties of the estimators. The methods are illustrated and their performance is compared in a simulation study. Finally, the methods are applied to a set of observations concerning sunspot data.PRODEP II
N-tree approximation for the largest Lyapunov exponent of a coupled-map lattice
The N-tree approximation scheme, introduced in the context of random directed
polymers, is here applied to the computation of the maximum Lyapunov exponent
in a coupled map lattice. We discuss both an exact implementation for small
tree-depth and a numerical implementation for larger s. We find that the
phase-transition predicted by the mean field approach shifts towards larger
values of the coupling parameter when the depth is increased. We conjecture
that the transition eventually disappears.Comment: RevTeX, 15 pages,5 figure
Dynamics and perturbations in assisted chaotic inflation
On compactification from higher dimensions, a single free massive scalar
field gives rise to a set of effective four-dimensional scalar fields, each
with a different mass. These can cooperate to drive a period of inflation known
as assisted inflation. We analyze the dynamics of the simplest implementation
of this idea, paying particular attention to the decoupling of fields from the
slow-roll regime as inflation proceeds. Unlike normal models of inflation, the
dynamics does not become independent of the initial conditions at late times.
In particular, we estimate the density perturbations obtained, which retain a
memory of the initial conditions even though a homogeneous, spatially-flat
Universe is generated.Comment: 10 pages, revtex, 2 figure
The Kinetic Basis of Self-Organized Pattern Formation
In his seminal paper on morphogenesis (1952), Alan Turing demonstrated that
different spatio-temporal patterns can arise due to instability of the
homogeneous state in reaction-diffusion systems, but at least two species are
necessary to produce even the simplest stationary patterns. This paper is aimed
to propose a novel model of the analog (continuous state) kinetic automaton and
to show that stationary and dynamic patterns can arise in one-component
networks of kinetic automata. Possible applicability of kinetic networks to
modeling of real-world phenomena is also discussed.Comment: 8 pages, submitted to the 14th International Conference on the
Synthesis and Simulation of Living Systems (Alife 14) on 23.03.2014, accepted
09.05.201
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