Journal ArticleDOI
Continuous control of chaos by self-controlling feedback
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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.About:
This article is published in Physics Letters A.The article was published on 1992-11-23. It has received 2957 citations till now. The article focuses on the topics: Control of chaos & System dynamics.read more
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Feedback Induced Instability and Chaos in Semiconductor Lasers and Their Applications
TL;DR: In this paper, the dynamics of feedback induced instability and chaos, especially for optical feedback, and their applications are reviewed in a semiconductor laser with feedback is an excellent model for nonlinear optical system which shows chaotic dynamics.
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Control of chaos by nonfeedback methods in a simple electronic circuit system and the FitzHugh-Nagumo equation
TL;DR: A critical analysis of nonfeedback methods such as addition of constant bias, second periodic force, addition of weak periodic pulse, and entrainment control are applied to a simple electronic circuit, namely, the Murali-Lakshmanan-Chua circuit system and FitzHugh-Nagumo equation.
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Libration Control of Electrodynamic Tethers in Inclined Orbit
Jesús Peláez,E. C. Lorenzini +1 more
TL;DR: In this article, two control schemes have been analyzed for an electrodynamic tether working in an inclined orbit, where the background strategy is the same: add appropriate forces to the system with the aim of converting an unstable periodic orbit of the governing equations into an asymptotically stable one.
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Controlling dynamical systems using multiple delay feedback control
Alexander Ahlborn,Ulrich Parlitz +1 more
TL;DR: A comparison with delayed feedback control methods that are based on a single (fundamental) delay time shows that MDFC is more effective for fixed point stabilization in terms of stability and flexibility, in particular for large delay times.
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Strange attractors and chaos control in periodically forced complex Duffing's oscillators
TL;DR: In this paper, the problem of chaotic control for complex periodically forced systems of two degrees of freedom is studied. And the authors show that chaotic behavior in these models is verified by the existence of positive maximal Lyapunov exponent, which is a special form of a time-continuous perturbation.
References
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Deterministic nonperiodic flow
TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
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Synchronization in chaotic systems
TL;DR: This chapter describes the linking of two chaotic systems with a common signal or signals and highlights that when the signs of the Lyapunov exponents for the subsystems are all negative the systems are synchronized.
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An equation for continuous chaos
TL;DR: A prototype equation to the Lorenz model of turbulence contains just one (second-order) nonlinearity in one variable as mentioned in this paper, which allows for a "folded" Poincare map (horseshoe map).
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Driving systems with chaotic signals.
TL;DR: It is shown that driving with chaotic signals can be done in a robust fashion, rather insensitive to changes in system parameters, and the calculation of the stability criteria leads naturally to an estimate for the convergence of the driven system to its stable state.
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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.