5,239 research outputs found
Viewing the efficiency of chaos control
This paper aims to cast some new light on controlling chaos using the OGY-
and the Zero-Spectral-Radius methods. In deriving those methods we use a
generalized procedure differing from the usual ones. This procedure allows us
to conveniently treat maps to be controlled bringing the orbit to both various
saddles and to sources with both real and complex eigenvalues. We demonstrate
the procedure and the subsequent control on a variety of maps. We evaluate the
control by examining the basins of attraction of the relevant controlled
systems graphically and in some cases analytically
Stabilizing chaotic vortex trajectories: an example of high-dimensional control
A chaos control algorithm is developed to actively stabilize unstable
periodic orbits of higher-dimensional systems. The method assumes knowledge of
the model equations and a small number of experimentally accessible parameters.
General conditions for controllability are discussed. The algorithm is applied
to the Hamiltonian problem of point vortices inside a circular cylinder with
applications to an experimental plasma system.Comment: 15 LaTex pages, 4 Postscript figures adde
Controlling Chaos Faster
Predictive Feedback Control is an easy-to-implement method to stabilize
unknown unstable periodic orbits in chaotic dynamical systems. Predictive
Feedback Control is severely limited because asymptotic convergence speed
decreases with stronger instabilities which in turn are typical for larger
target periods, rendering it harder to effectively stabilize periodic orbits of
large period. Here, we study stalled chaos control, where the application of
control is stalled to make use of the chaotic, uncontrolled dynamics, and
introduce an adaptation paradigm to overcome this limitation and speed up
convergence. This modified control scheme is not only capable of stabilizing
more periodic orbits than the original Predictive Feedback Control but also
speeds up convergence for typical chaotic maps, as illustrated in both theory
and application. The proposed adaptation scheme provides a way to tune
parameters online, yielding a broadly applicable, fast chaos control that
converges reliably, even for periodic orbits of large period
Controlling chaos in area-preserving maps
We describe a method of control of chaos that occurs in area-preserving maps.
This method is based on small modifications of the original map by addition of
a small control term. We apply this control technique to the standard map and
to the tokamap
Adapting Predictive Feedback Chaos Control for Optimal Convergence Speed
Stabilizing unstable periodic orbits in a chaotic invariant set not only
reveals information about its structure but also leads to various interesting
applications. For the successful application of a chaos control scheme,
convergence speed is of crucial importance. Here we present a predictive
feedback chaos control method that adapts a control parameter online to yield
optimal asymptotic convergence speed. We study the adaptive control map both
analytically and numerically and prove that it converges at least linearly to a
value determined by the spectral radius of the control map at the periodic
orbit to be stabilized. The method is easy to implement algorithmically and may
find applications for adaptive online control of biological and engineering
systems.Comment: 21 pages, 6 figure
Bailout Embeddings, Targeting of KAM Orbits, and the Control of Hamiltonian Chaos
We present a novel technique, which we term bailout embedding, that can be
used to target orbits having particular properties out of all orbits in a flow
or map. We explicitly construct a bailout embedding for Hamiltonian systems so
as to target KAM orbits. We show how the bailout dynamics is able to lock onto
extremely small KAM islands in an ergodic sea.Comment: 3 figures, 9 subpanel
Drift and its mediation in terrestrial orbits
The slow deformation of terrestrial orbits in the medium range, subject to
lunisolar resonances, is well approximated by a family of Hamiltonian flow with
degree-of-freedom. The action variables of the system may experience
chaotic variations and large drift that we may quantify. Using variational
chaos indicators, we compute high-resolution portraits of the action space.
Such refined meshes allow to reveal the existence of tori and structures
filling chaotic regions. Our elaborate computations allow us to isolate precise
initial conditions near specific zones of interest and study their asymptotic
behaviour in time. Borrowing classical techniques of phase- space
visualisation, we highlight how the drift is mediated by the complement of the
numerically detected KAM tori.Comment: 22 pages, 11 figures, 1 table, 52 references. Comments and feedbacks
greatly appreciated. This article is part of the Research Topic `The
Earth-Moon System as a Dynamical Laboratory', confer
https://www.frontiersin.org/research-topics/5819/the-earth-moon-system-as-a-dynamical-laborator
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