Control of NMR-laser chaos in high-dimensional embedding space

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsPublished 1 January 1993

Charles Reyl, L. Flepp, R. Badii, E. Brun

DOI10.1103/physreve.47.267

Citations62

TL;DR

An improved method has been implemented in order to circumvent the occurrence of several, possibly complex, unstable eigenvalues in the standard OGY procedure and has shown superior performance.

Abstract

The unstable periodic orbits of a chaotic NMR laser have been identified and classified according to their stability properties. The dynamical control method by Ott, Grebogi, and Yorke (OGY) [Phys. Rev. Lett. 64, 1196 (1990)] has been successfully applied in a six-dimensional embedding space, as required for a proper reconstruction of the attractors. An improved method has then been implemented in order to circumvent the occurrence of several, possibly complex, unstable eigenvalues in the standard OGY procedure and has shown superior performance. Finally, an extension to several control stations per Poincaré time is discussed.

Keywords

Computer SciencePhysics and Astronomy

Physical Review LettersControlling chaos

5,373 Citations1990Edward Ott, Celso Grebogi +1 more

Physical Review LettersExperimental control of chaos

709 Citations1990William L. Ditto, S. N. Rauseo +1 more

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.

Physical Review LettersDynamical control of a chaotic laser: Experimental stabilization of a globally coupled system

529 Citations1992Rajarshi Roy, Thomas W Murphy +3 more

It is shown that complex periodic wave forms can be stabilized in the laser output intensity, indicating that this control technique may bewidely applicable to autonomous, higher-dimensional chaotic systems, including globally coupled arrays of nonlinear oscillators.

Physical Review LettersControlling a chaotic system

350 Citations1991Jack W. Singer, Yizhen Wang +1 more

Using both experimental and theoretical results, this Letter describes how low-energy, feedback control signals can be successfully utilized to suppress (laminarize) chaotic flow in a thermal convection loop.

Physical Review LettersControlling chaos using time delay coordinates

275 Citations1992U. Dressler, Gregor Nitsche

This chapter discusses controlling chaos using time delay coordinates, a new method of controlling a chaotic dynamical system by stabilizing one of the many unstable periodic orbits embedded in a chaotic attractor through only small time dependent perturbations in some accessible system parameter.

Physical Review LettersControlling chaos in spin-wave instabilities

184 Citations1991Antonio Azevedo, S. M. Rezende

A microwave-pumped spin-wave-instability experiment is used to demonstrate that chaos can be controlled by a small periodic perturbation of an available system parameter, as recently proposed by Ott, Grebogi, and Yorke.

Physical review. A, General physicsNoise reduction in dynamical systems

162 Citations1988Eric J. Kostelich, James A. Yorke

Physica D Nonlinear PhenomenaPeriodic entrainment of chaotic logistic map dynamics

118 Citations1990E. Atlee Jackson, Alfred Hübler

Journal of the Optical Society of America BObservation of order and chaos in a nuclear spin–flip laser

104 Citations1985E. Brun, B. Derighetti +3 more

Physical Review LettersModel identification by periodic-orbit analysis for NMR-laser chaos

43 Citations1991L. Flepp, R. Holzner +3 more

It is shown that the conventional Bloch-Kirchhoff description of NMR-laser activity needs the inclusion of a nonlinear relaxation term for the transverse magnetization in order to account for the experimental observation.