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Synchronization of chaotic oscillators in a generalized sense leads to richer behavior than identical chaotic oscillations in coupled systems. It may imply a more complicated connection between the synchronized trajectories in the state spaces of coupled systems. We suggest a method here that can be used to detect and study generalized synchronization in drive-response systems. This technique, the auxiliary system method, utilizes a second, identical response system to monitor the synchronized motions. The method can be implemented both numerically and experimentally and in some cases it leads to analytical results for generalized synchronization. ͓S1063-651X͑96͒02505-6͔

Using chaotic signals in spread-spectrum communications has a few clear advantages over traditional approaches. Chaotic signals are nonperiodic, wide-band, and more difficult to predict, reconstruct, and characterize than periodic carriers. These properties of chaotic signals make it more difficult to intercept and decode the information modulated upon them. However, many suggested chaos-based communication schemes do not provide processing gain, a feature highly desirable in spread-spectrum communication schemes. In this paper, we suggest two communication schemes that provide a processing gain. The performance of these and of the earlier proposed differential chaos shift keying is studied analytically and numerically for discrete time implementations. It is shown that, when performance is characterized by the dependence of bit error rate on 0 , the increase of the spreading sequence length beyond a certain point degrades the performance. For a given 0 , there is a length of the spreading sequence that minimizes the bit error rate.

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