Secure communications and unstable periodic orbits of strange attractors

Abstract

Every chaotic attractor is thought to be composed of the collection of unstable manifolds of all its unstable periodic orbits (UPOs). These UPOs can be used for communication by amplitude or phase modulation just as one would modulate stable periodic orbits (resonant frequencies of a linear system or limit cycles-in a nonlinear system). Using UPOs for communications has a variety of benefits. Since a chaotic attractor contains an infinite number of UPOs, a single time series can carry many different messages by placing each one on a different UPO. Because UPOs are topological properties of a chaotic attractor, the signal has a natural noise immunity, and receipt of a signal should be robust to moderate differences between the transmitter and receiver parameters. >