Stabilizing unstable periodic orbits in fast dynamical systems
- 1 October 1994
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 50 (4) , 3245-3248
- https://doi.org/10.1103/physreve.50.3245
Abstract
We present a technique for stabilizing unstable periodic orbits in low-dimensional dynamical systems that allows for control over a large domain of parameters. The technique uses a continuous feedback loop incorporating information from many previous states of the system in a form closely related to the amplitude of light reflected from a Fabry-Pérot interferometer. We demonstrate that the approach is well suited for pratical implementation in fast systems by stabilizing a chaotic diode resonator driven at 10.1 MHz.Keywords
This publication has 27 references indexed in Scilit:
- Numerical integration of ordinary differential equations on manifoldsJournal of Nonlinear Science, 1993
- FROM CHAOS TO ORDER — PERSPECTIVES AND METHODOLOGIES IN CONTROLLING CHAOTIC NONLINEAR DYNAMICAL SYSTEMSInternational Journal of Bifurcation and Chaos, 1993
- Mastering ChaosScientific American, 1993
- Using small perturbations to control chaosNature, 1993
- Controlling chaotic dynamical systemsPhysica D: Nonlinear Phenomena, 1992
- Dynamical control of a chaotic laser: Experimental stabilization of a globally coupled systemPhysical Review Letters, 1992
- Stabilizing high-period orbits in a chaotic system: The diode resonatorPhysical Review Letters, 1991
- Controlling a chaotic systemPhysical Review Letters, 1991
- Experimental control of chaosPhysical Review Letters, 1990
- Controlling chaosPhysical Review Letters, 1990