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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Chaotic motion and its control for nonlinear nonplanar oscillations of a parametrically excited cantilever beam
TL;DR: In this article, a new method of controlling chaotic motion for the nonlinear nonplanar oscillations of the cantilever beam, refereed as to the force control approach, is proposed for the first time.
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Bifurcation continuation, chaos and chaos control in nonlinear Bloch system
TL;DR: In this paper, a detailed analysis of the stability and bifurcation pattern of the nonlinear Bloch equation known to govern the dynamics of an ensemble of spins, controlling the basic process of nuclear magnetic resonance is undertaken.
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Feedback suppression of neural synchrony in two interacting populations by vanishing stimulation.
TL;DR: It is demonstrated that the feedback loop, organized in this way, provides an efficient suppression of collective synchrony in a system of two interacting oscillatory networks, and provides a vanishing-stimulation control.
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Analytic programming in the task of evolutionary synthesis of a controller for high order oscillations stabilization of discrete chaotic systems
TL;DR: This paper deals with the utilization of a symbolic regression tool, which is Analytic Programming (AP), together with two evolutionary algorithms, the Self-Organizing Migrating Algorithm (SOMA) and Differential Evolution (DE), for the synthesis of a new control law.
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Control of the chaotic regimes of nonlinear drift-waves in a magnetized laboratory plasma
TL;DR: Pyragas et al. as discussed by the authors experimentally studied nonlinear drift-waves in a cylindrical magnetized laboratory plasma and controled low-dimensional chaotic regimes using the time-delay autosynchronization method.
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.