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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Stabilization of an unstable steady state in a Mackey-Glass system
TL;DR: In this paper, theoretical and experimental results of stabilizing an unstable steady state in a Mackey-glass system and its electronic analog driven into regions of hyperchaotic oscillations are presented.
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Controlling chaos in a fast diode resonator using extended time-delay autosynchronization: Experimental observations and theoretical analysis
TL;DR: It is shown that increasing the weights given to temporally distant states enlarges thedomain of control and reduces the sensitivity of the domain of control on the propagation delays in the feedback loop, and it is determined the average time to obtain control as a function of the feedback gain.
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Nonlinear dynamics and chaotic control of a flexible multibody system with uncertain joint clearance
TL;DR: In this paper, the nonlinear dynamics of a flexible multibody system with interval clearance size in a revolute joint is investigated, and the influence of the Lund-Grenoble and the modified Coulomb's friction models on the system dynamics is comparatively studied.
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Difference feedback can stabilize uncertain steady states
TL;DR: A dynamic output difference feedback is shown to be able to stabilize under quite a mild condition that the steady state is not associated with zero eigenvalues, illustrated by using a cart-pendulum system which moves along a one dimensional varying slope.
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Dynamics of a limit cycle oscillator under time delayed linear and nonlinear feedbacks
TL;DR: In this article, the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator were investigated and a host of complex temporal phenomena such as phase slips, frequency suppression, multiple periodic states and chaos were observed in a large number of coupled limit cycle oscillators.
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.