Journal ArticleDOI
Continuous control of chaos by self-controlling feedback
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TLDR
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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Synchronization of two coupled self-excited systems with multi-limit cycles
TL;DR: The stability and optimization of the synchronization process between two coupled self-excited systems modeled by the multi-limit cycles van der Pol oscillators through the case of an enzymatic substrate reaction with ferroelectric behavior in brain waves model is analyzed.
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Chaos control of a nonlinear oscillator with shape memory alloy using an optimal linear control: Part II: Nonideal energy source
TL;DR: In this paper, an optimal linear control technique was applied to suppress chaotic behavior in a SMA oscillator, driven by a DC motor with limited power supply (nonideal sources), and the efficiency of the method in resonance region was evaluated.
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A stable-manifold-based method for chaos control and synchronization
TL;DR: In this article, a stable manifold-based method for chaotic control and synchronization is proposed, where the goal is only to force the system state to lie on the selected stable manifold.
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A novel artificial bee colony algorithm with space contraction for unknown parameters identification and time-delays of chaotic systems
TL;DR: Simulation results demonstrate that ABCSC is superior to ABC and HTCMIABC for unknown parameters and time-delays of the chaotic systems accurately and effectively and is a promising tool for chaotic system identification as well as other numerical optimization problems in mathematics.
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Control of chaos in delay differential equations, in a network of oscillators and in model cortex
TL;DR: In this paper, the Ott-Grebogi-Yorke method was extended to the stabilization of unstable orbits in a network of oscillators exhibiting spatiotemporal chaotic activity, wherein the perturbation is applied to the variables of the system.
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.