Transmission of Signals via Synchronization of Chaotic Time-delay Systems

Synchronization of chaotic systems has aroused much interest in recent years, particularly in light of potential application of this phenomenon in secure communication. Different approaches for constructing synchronized chaotic systems are proposed. Among them is the approach of Pecora and Carroll [1990] who show that when a state variable from a chaotically evolving system is transmitted as an input to a replica of part of the original system, the replica subsystem (receiver) can synchronize to the original system (sender). To use this phenomenon for masking messages one can transmit to the receiver a summary signal consisting of a chaotic signal generated by sender and a small information signal containing a message [Kocarev et al., 1992]. Then the message can be recovered by synchronizing the receiver with the scalar signal which is transmitted from the sender. The shortcoming of this approach is that the information signal violates the synchrony between sender and receiver giving rise to reconstruction errors in the recovered information. Recently, Kocarev and Parlitz [1995] have proposed a generalization of the Pecora and Carroll [1990] method, which extends the capabilities for constructing synchronized chaotic systems. This new approach enables the information signal to be integrated in the sender as a driving signal. The scalar signal which is transmitted from the sender to the receiver is a function of the sender state variables and the information signal. At ideal conditions the information signal can be recovered exactly, without the reconstruction errors. Most theoretical as well as experimental studies of secure communication reported so far concern low-dimensional systems with one positive Lyapunov exponent. Perez and Cerdeira [1995] have shown that messages masked by such simple chaotic processes, once intercepted, can be sometimes readily extracted. To improve security it is desirable to use high-dimensional systems with multiple positive Lyapunov exponents (hyperchaotic systems) which take advantage of the increased randomness and unpredictability. Recently, Peng et al. [1996] have demonstrated the possibility of synchronizing hyperchaotic systems by transmitting just a single scalar variable composed of a linear combination of state variables of the sender. Another way of synthesizing synchronized hyperchaotic systems using a series of low-dimensional subsystems as building blocks has been proposed by Kocarev and Parlitz [1995]. These methods have many advantages, but they have been applied only to finite-dimensional systems described by ordinary differential equations