SECURE COMMUNICATIONS AND UNSTABLE PERIODIC-ORBITS OF STRANGE ATTRACTORS

Every chaotic attractor is thought to be composed of the collection of unstable manifolds of all its unstable periodic orbits (UPO's). These UPO's 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 UPO's for communications has a variety of benefits. Since a chaotic attractor contains an infinite number of UPO's, a single time series can carry many different messages by placing each one on a different UPO. Because UPO's are topological properties of a chaotic attractor, the signal has a natural noise immunity, and receipt of a should be robust to moderate differences between the transmitter and receiver parameters.