7,465 research outputs found
The Control of Dynamical Systems - Recovering Order from Chaos -
Following a brief historical introduction of the notions of chaos in
dynamical systems, we will present recent developments that attempt to profit
from the rich structure and complexity of the chaotic dynamics. In particular,
we will demonstrate the ability to control chaos in realistic complex
environments. Several applications will serve to illustrate the theory and to
highlight its advantages and weaknesses. The presentation will end with a
survey of possible generalizations and extensions of the basic formalism as
well as a discussion of applications outside the field of the physical
sciences. Future research avenues in this rapidly growing field will also be
addressed.Comment: 18 pages, 9 figures. Invited Talk at the XXIth International
Conference on the Physics of Electronic and Atomic Collisions (ICPEAC), July
22-27, 1999 (Sendai, Japan
Recurrent flow analysis in spatiotemporally chaotic 2-dimensional Kolmogorov flow
Motivated by recent success in the dynamical systems approach to transitional
flow, we study the efficiency and effectiveness of extracting simple invariant
sets (recurrent flows) directly from chaotic/turbulent flows and the potential
of these sets for providing predictions of certain statistics of the flow.
Two-dimensional Kolmogorov flow (the 2D Navier-Stokes equations with a
sinusoidal body force) is studied both over a square [0, 2{\pi}]2 torus and a
rectangular torus extended in the forcing direction. In the former case, an
order of magnitude more recurrent flows are found than previously (Chandler &
Kerswell 2013) and shown to give improved predictions for the dissipation and
energy pdfs of the chaos via periodic orbit theory. Over the extended torus at
low forcing amplitudes, some extracted states mimick the statistics of the
spatially-localised chaos present surprisingly well recalling the striking
finding of Kawahara & Kida (2001) in low-Reynolds-number plane Couette flow. At
higher forcing amplitudes, however, success is limited highlighting the
increased dimensionality of the chaos and the need for larger data sets.
Algorithmic developments to improve the extraction procedure are discussed
Shil'nikov Chaos control using Homoclinic orbits and the Newhouse region
A method of controlling Shil'nikov's type chaos using windows that appear in
the 1 dimensional bifurcation diagram when perturbations are applied, and using
existence of stable homoclinic orbits near the unstable one is presented and
applied to the electronic Chua's circuit. A demonstration of the chaos control
in the electronic circuit experiments and their simulations and bifurcation
analyses are given.Comment: 23 pages, 48 figure
Controlling chaos in spatially extended beam-plasma system by the continuous delayed feedback
In present paper we discuss the control of complex spatio-temporal dynamics
in a {spatially extended} non-linear system (fluid model of Pierce diode) based
on the concepts of controlling chaos in the systems with few degrees of
freedom. A presented method is connected with stabilization of unstable
homogeneous equilibrium state and the unstable spatio-temporal periodical
states analogous to unstable periodic orbits of chaotic dynamics of the systems
with few degrees of freedom. We show that this method is effective and allows
to achieve desired regular dynamics chosen from a number of possible in the
considered system.Comment: 12 pages, 12 figure
Controlling chaos in diluted networks with continuous neurons
Diluted neural networks with continuous neurons and nonmonotonic transfer
function are studied, with both fixed and dynamic synapses. A noisy stimulus
with periodic variance results in a mechanism for controlling chaos in neural
systems with fixed synapses: a proper amount of external perturbation forces
the system to behave periodically with the same period as the stimulus.Comment: 11 pages, 8 figure
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