Stabilizing high-period orbits in a chaotic system: The diode resonator

Abstract

The chaotic dynamics found in the diode resonator has been converted into stable orbits with periods up to 23 drive cycles long. The method used is a modification of that of Ott, Grebogi, and Yorke [Phys. Rev. Lett. 64, 1196 (1990)]. In addition to stabilizing existing low-period orbits, the method allows making small alterations in the attractor permitting previously nonexistent periodic orbits to be stabilized. It is an analog technique and therefore can be very fast, making it applicable to a wide variety of systems.