Journal ArticleDOI
Experimental control of chaos by delayed self-controlling feedback
Kestutis Pyragas,A. Tamaševičius +1 more
TLDR
Pyragas as discussed by the authors proposed a method for chaos control by a small time-continuous perturbation, which is realized experimentally by a specially designed analogue circuit using a simple delay line.About:
This article is published in Physics Letters A.The article was published on 1993-08-30. It has received 322 citations till now.read more
Citations
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Journal ArticleDOI
The control of chaos: theory and applications
TL;DR: In this paper, the Ott-Grebogi-Yorke (OGY) method and the adaptive method for chaotic control are discussed. But the authors focus on the targeting problem, i.e., how to bring a trajectory to a small neighborhood of a desired location in the chaotic attractor in both low and high dimensions.
Journal ArticleDOI
Control of chaos via extended delay feedback
TL;DR: In this paper, a linear analysis for a modification of the delay feedback control technique that allows one to stabilize unstable periodic orbits of a strange attractor over a large domain of parameters is presented.
Journal ArticleDOI
Control of Chaos via an Unstable Delayed Feedback Controller
TL;DR: A modified scheme based on an unstable delayed feedback controller for stabilizing unstable periodic orbits embedded in chaotic attractors and shows efficiency for an unstable fixed point of a simple dynamic model and an unstable periodic orbit of the Lorenz system.
Journal ArticleDOI
Delayed feedback control of chaos.
TL;DR: Recent advancements in the theory, as well as an idea of using an unstable degree of freedom in a feedback loop to avoid a well-known topological limitation of the method, are described in detail.
Journal ArticleDOI
Limitation of delayed feedback control in nonlinear discrete-time systems
TL;DR: In this paper, it was shown that a fixed point can not be stabilized by the delayed state-feedback control if the linearized system around the fixed point has an odd number of real eigenvalues greater than one.
References
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Journal ArticleDOI
Continuous control of chaos by self-controlling feedback
TL;DR: In this paper, the stabilization of unstable periodic orbits of a chaotic system is achieved either by combined feedback with the use of a specially designed external oscillator, or by delayed self-controlling feedback without using of any external force.
Journal ArticleDOI
Experimental control of chaos.
TL;DR: It was demonstrated that one can convert the motion of a chaotic dynamical system to periodic motion by controlling the system about one of the many unstable periodic orbits embedded in the chaotic attractor, through only small time dependent perturbations in an accessible system parameter.
Journal ArticleDOI
Stabilizing high-period orbits in a chaotic system: The diode resonator.
TL;DR: In this article, the chaotic dynamics found in the diode resonator have been converted into stable orbits with periods up to 23 drive cycles long, using a modification of that of Ott, Grebogi, and Yorke.
Journal ArticleDOI
Controlling chaotic dynamical systems
TL;DR: In this paper, the authors describe a method that converts the motion on a chaotic attractor to a desired attracting time periodic motion by making only small time dependent perturbations of a control parameter.
Journal ArticleDOI
Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled system.
TL;DR: It is shown that complex periodic wave forms can be stabilized in the laser output intensity, indicating that this control technique may bewidely applicable to autonomous, higher-dimensional chaotic systems, including globally coupled arrays of nonlinear oscillators.