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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Proceedings ArticleDOI
Feedback control via eigenvalue assignment for time delayed systems using the lambert w function
TL;DR: In this article, the problem of feedback controller design via eigenvalue assignment for systems of linear delay differential equations (DDEs) was considered, and a solution to linear DDEs in terms of the matrix Lambert W function was proposed.
Journal ArticleDOI
Hopf Bifurcation, Positively Invariant Set, and Physical Realization of a New Four-Dimensional Hyperchaotic Financial System
TL;DR: In this article, a new four-dimensional hyperchaotic financial system on the basis of an established three-dimensional nonlinear financial system and a dynamic model by adding a controller term to consider the effect of control on the system was introduced.
Journal ArticleDOI
Delayed Feedback Versus Seasonal Forcing: Resonance Phenomena in an El Nin͂o Southern Oscillation Model
TL;DR: This work considers a phenomenological model for the El Nino Southern Oscillation system, where the delayed effects of oceanic waves are incorporated explicitly into the model, and presents exemplary stable solutions of the model.
Journal ArticleDOI
Global manifold control in a driven laser: sustaining chaos and regular dynamics
R. Meucci,D. Cinotti,Enrico Allaria,Lora Billings,Ioana Triandaf,David S. Morgan,Ira B. Schwartz +6 more
TL;DR: In this paper, the authors present experimental and numerical evidence of a multi-frequency phase control able to preserve periodic behavior within a chaotic window as well as to re-excite chaotic behavior when it is destroyed by the presence of a mitigating unstable periodic orbit created by the multiscale drive.
Journal ArticleDOI
An experimental realization of a pulsed control method for the KSS chaotic circuit
Jose Francisco Moreno Verdulla,Manuel J. López Sánchez,Manuel Prian,José M. Lorenzo,Luis Antonio Feliciano García +4 more
TL;DR: A method for controlling chaotic systems by means of pulses, with four variants, is presented, and its real time application to a particular electronic chaotic circuit (Kiers-Schmidt-Sprott, KSS) is analyzed.
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).
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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.