Stabilizing unstable periodic orbits in fast dynamical systems

This work presents a technique for stabilizing unstable periodic orbits in low-dimensional dynamical systems that allows for control over a large domain of parameters and demonstrates that the approach is well suited for pratical implementation in fast systems by stabilizing a chaotic diode resonator driven at 10.1 MHz.

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-P\'erot 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.