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
Citations
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On analytical properties of delayed feedback control of chaos
TL;DR: In this article, two theorems on limitations in controlling chaos by delayed feedback control are proved, and the results are as follows: (1) if the linear variational equation about the target hyperbolic unstable periodic orbit (UPO) has an odd number of real characteristic multipliers which is greater than unity, the UPO can never be stabilized with any value of the feedback gain.
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Control of Chaos: Methods and Applications. I. Methods
TL;DR: The problems and methods of control of chaos, which in the last decade was the subject of intensive studies, were reviewed and the basic results obtained within the framework of the traditional linear, nonlinear, and adaptive control, as well as the neural network systems and fuzzy systems were presented.
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Synchronization of Genesio chaotic system via backstepping approach
TL;DR: In this paper, an adaptive backstepping control law is derived to make the error signals between drive Genesio system and response Gensio system with an uncertain parameter asymptotically synchronized.
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Controlling and synchronizing chaotic Genesio system via nonlinear feedback control
Maoyin Chen,Zhengzhi Han +1 more
TL;DR: A nonlinear feedback controller is designed to make the controlled system be stabilized at origin and two Genesio systems be synchronized and the stability analysis of controlled system becomes simple Hurwitz stability analysis provided that a parameter is chosen suitably.
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Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback
TL;DR: Theoretical and experimental investigations of chaos synchronization and its application to chaotic data transmissions in semiconductor lasers with optical feedback are presented in this article, where the conditions for chaos synchronization in the systems and the robustness for the parameter mismatches are studied.
References
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Journal ArticleDOI
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.