Synchronization of delay-differential equations with application to private communication

Unidirectional synchronization of high-dimensional chaos with many positive Lyapunov exponents is demonstrated in first-order delay-differential equations (DDEs) at large delays. Synchronization of this hyperchaotic motion is shown to occur using feedback involving only one scalar variable. An analysis of the potential usefulness of such simple yet infinite-dimensional dynamical systems for broadband signal masking and private communication is also given. A particular feature is the chaotic masking of finite messages encoded onto controlled unstable periodic orbits of the same DDE dynamics used to generate the masking chaos. The difference equation obtained in the singular limit can further be used to transmit digital messages and predict the parameter range over which synchronization in the DDE occurs. Results for systems with a distribution of delays are also presented. (C) 1998 Elsevier Science B.V.