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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Journal ArticleDOI
Stabilizing the unstable periodic orbits of a hybrid chaotic system using optimal control
TL;DR: The idea consists in stabilizing a predetermined orbit of a given length by using an optimal control method to determine the switching instants from one subsystem to the other while minimizing the difference between two successive orbits.
Book ChapterDOI
Oscillations, Synchrony and DeterministicChaos
TL;DR: The ordered complexity of biological systems out-performs the simplicity of physical or chemical systems and its basic understanding remains a challenge despite recent successes in imaging and the increasing power of analytical chemistry.
Book ChapterDOI
Control of chemical wave propagation
TL;DR: Using the Schl\"{o}gl model as a paradigmatic example of a bistable reaction-diffusion system, the authors discuss some physically feasible options of open and closed loop spatio-temporal control of chemical wave propagation.
Journal ArticleDOI
A Novel non-Lyapunov way for detecting uncertain parameters of chaos system with random noises
TL;DR: A scheme based on differential evolution algorithm (DE) is newly introduced to solve the problem via a nonnegative multi-modal nonlinear optimization, which finds a best combination of parameters and time-delays such that an objective function is minimized.
Journal ArticleDOI
Time delay Duffing’s systems: chaos and chatter control
TL;DR: In this paper, the effect of a delay feedback control (DFC) realized by displacement in the Duffing oscillator, for parameters which generate strange chaotic Ueda attractor is investigated.
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.
Journal ArticleDOI
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).
Journal ArticleDOI
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.
Journal ArticleDOI
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.