13,703 research outputs found
A two-variable approach to solve the polynomial Lyapunov equation
A two-variable polynomial approach to solve the one-variable polynomial Lyapunov equation is proposed. Lifting the problem from the one-variable to the two-variable context allows to use Faddeev-type recursions in order to solve the polynomial Lyapunov equation in an iterative fashion. The method is especially suitable for applications requiring exact or symbolic computation
Macroscopic chaos in globally coupled maps
We study the coherent dynamics of globally coupled maps showing macroscopic
chaos. With this term we indicate the hydrodynamical-like irregular behaviour
of some global observables, with typical times much longer than the times
related to the evolution of the single (or microscopic) elements of the system.
The usual Lyapunov exponent is not able to capture the essential features of
this macroscopic phenomenon. Using the recently introduced notion of finite
size Lyapunov exponent, we characterize, in a consistent way, these macroscopic
behaviours. Basically, at small values of the perturbation we recover the usual
(microscopic) Lyapunov exponent, while at larger values a sort of macroscopic
Lyapunov exponent emerges, which can be much smaller than the former. A
quantitative characterization of the chaotic motion at hydrodynamical level is
then possible, even in the absence of the explicit equations for the time
evolution of the macroscopic observables.Comment: 24 pages revtex, 9 figures included. Improved version also with 1
figure and some references adde
Quantum control theory and applications: A survey
This paper presents a survey on quantum control theory and applications from
a control systems perspective. Some of the basic concepts and main developments
(including open-loop control and closed-loop control) in quantum control theory
are reviewed. In the area of open-loop quantum control, the paper surveys the
notion of controllability for quantum systems and presents several control
design strategies including optimal control, Lyapunov-based methodologies,
variable structure control and quantum incoherent control. In the area of
closed-loop quantum control, the paper reviews closed-loop learning control and
several important issues related to quantum feedback control including quantum
filtering, feedback stabilization, LQG control and robust quantum control.Comment: 38 pages, invited survey paper from a control systems perspective,
some references are added, published versio
Predictability: a way to characterize Complexity
Different aspects of the predictability problem in dynamical systems are
reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy,
Shannon entropy and algorithmic complexity is discussed. In particular, we
emphasize how a characterization of the unpredictability of a system gives a
measure of its complexity. Adopting this point of view, we review some
developments in the characterization of the predictability of systems showing
different kind of complexity: from low-dimensional systems to high-dimensional
ones with spatio-temporal chaos and to fully developed turbulence. A special
attention is devoted to finite-time and finite-resolution effects on
predictability, which can be accounted with suitable generalization of the
standard indicators. The problems involved in systems with intrinsic randomness
is discussed, with emphasis on the important problems of distinguishing chaos
from noise and of modeling the system. The characterization of irregular
behavior in systems with discrete phase space is also considered.Comment: 142 Latex pgs. 41 included eps figures, submitted to Physics Reports.
Related information at this http://axtnt2.phys.uniroma1.i
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