Cupolets and a Chaotic Analog of Entanglement

TL;DR

This paper explores the stabilization of chaotic systems using cupolets, a control technique that can identify and stabilize unstable periodic orbits, with potential applications in secure communication and an analogy to quantum entanglement.

Contribution

It introduces a method to induce mutual stabilization of chaotic systems using cupolets, proposing an analog to quantum entanglement in classical chaos control.

Findings

Cupolets can be used for data compression and secure communication.

Two interacting chaotic systems can be stabilized into a mutual state.

An analog of quantum entanglement is demonstrated in classical chaos.

Abstract

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.