Cupolets and a Chaotic Analog of Entanglement

This paper discusses applications of a particular control technique that can be used to very efficiently stabilize a chaotic system onto a large subset of the unstable periodic orbits that are typically embedded in the system. The control method is adapted from one developed by Hayes, Grebogi, and Ott, and the resulting (stabilized) orbits are known as cupolets (Chaotic, Unstable, Periodic, Orbit-LETS). Cupolets exhibit the interesting property that a given set of controls will uniquely identify a cupolet, independent of its initial condition. Practical applications of cupolets already include data compression, secure communication, and image processing. We demonstrate how cupolets from two interacting chaotic systems may be induced into a state of mutual and self-sustaining stabilization, in a manner that may be an analog of quantum entanglement.