16 research outputs found
Variable-delay feedback control of unstable steady states in retarded time-delayed systems
We study the stability of unstable steady states in scalar retarded
time-delayed systems subjected to a variable-delay feedback control. The
important aspect of such a control problem is that time-delayed systems are
already infinite-dimensional before the delayed feedback control is turned on.
When the frequency of the modulation is large compared to the system's
dynamics, the analytic approach consists of relating the stability properties
of the resulting variable-delay system with those of an analogous distributed
delay system. Otherwise, the stability domains are obtained by a numerical
integration of the linearized variable-delay system. The analysis shows that
the control domains are significantly larger than those in the usual
time-delayed feedback control, and that the complexity of the domain structure
depends on the form and the frequency of the delay modulation.Comment: 13 pages, 8 figures, RevTeX, accepted for publication in Physical
Review
Stabilization of unstable steady states by variable delay feedback control
We report on a dramatic improvement of the performance of the classical
time-delayed autosynchronization method (TDAS) to control unstable steady
states, by applying a time-varying delay in the TDAS control scheme in a form
of a deterministic or stochastic delay-modulation in a fixed interval around a
nominal value . The successfulness of this variable delay feedback control
(VDFC) is illustrated by a numerical control simulation of the Lorenz and
R\"{o}ssler systems using three different types of time-delay modulations: a
sawtooth wave, a sine wave, and a uniform random distribution. We perform a
comparative analysis between the VDFC method and the standard TDAS method for a
sawtooth-wave modulation by analytically determining the domains of control for
the generic case of an unstable fixed point of focus type.Comment: 7 pages, 4 figures, RevTe
Exact Curie temperature for the Ising model on Archimedean and Laves lattices
Using the Feynman-Vdovichenko combinatorial approach to the two dimensional
Ising model, we determine the exact Curie temperature for all two dimensional
Archimedean lattices. By means of duality, we extend our results to cover all
two dimensional Laves lattices. For those lattices where the exact critical
temperatures are not exactly known yet, we compare them with Monte Carlo
simulations.Comment: 10 pages, 1 figures, 3 table
First-order phase transition in a 2D random-field Ising model with conflicting dynamics
The effects of locally random magnetic fields are considered in a
nonequilibrium Ising model defined on a square lattice with nearest-neighbors
interactions. In order to generate the random magnetic fields, we have
considered random variables that change randomly with time according to
a double-gaussian probability distribution, which consists of two single
gaussian distributions, centered at and , with the same width
. This distribution is very general, and can recover in appropriate
limits the bimodal distribution () and the single gaussian one
(). We performed Monte Carlo simulations in lattices with linear sizes in
the range . The system exhibits ferromagnetic and paramagnetic
steady states. Our results suggest the occurence of first-order phase
transitions between the above-mentioned phases at low temperatures and large
random-field intensities , for some small values of the width .
By means of finite size scaling, we estimate the critical exponents in the
low-field region, where we have continuous phase transitions. In addition, we
show a sketch of the phase diagram of the model for some values of .Comment: 13 pages, 9 figures, accepted for publication in JSTA
Direct algebraic mapping transformation for decorated spin models
In this article we propose a general transformation for decorated spin
models. The advantage of this transformation is to perform a direct mapping of
a decorated spin model onto another effective spin thus simplifying algebraic
computations by avoiding the proliferation of unnecessary iterative
transformations and parameters that might otherwise lead to transcendental
equations. Direct mapping transformation is discussed in detail for decorated
Ising spin models as well as for decorated Ising-Heisenberg spin models, with
arbitrary coordination number and with some constrained Hamiltonian's parameter
for systems with coordination number larger than 4 (3) with (without) spin
inversion symmetry respectively. In order to illustrate this transformation we
give several examples of this mapping transformation, where most of them were
not explored yet.Comment: 14 pages, 10 figure
Period p-tuplings in coupled maps
We study the critical behavior (CB) of all period -tuplings in symmetrically coupled
one-dimensional maps. We first investigate the CB for the case of two
coupled maps, using a renormalization method. Three (five) kinds of fixed
points of the renormalization transformation and their relevant ``coupling
eigenvalues'' associated with coupling perturbations are found in the case of
even (odd) . We next study the CB for the linear- and nonlinear-coupling
cases (a coupling is called linear or nonlinear according to its leading term),
and confirm the renormalization results. Both the structure of the critical set
(set of the critical points) and the CB vary according as the coupling is
linear or nonlinear. Finally, the results of the two coupled maps are extended
to many coupled maps with , in which the CB depends on the range of
coupling.Comment: RevTeX, 30 figures available upon reques