Amplitude-independent chaotic synchronization

There has recently been speculation on whether or not chaotic synchronization might be useful for communications. One problem with using chaotic synchronization to communicate is that the response system is nonlinear, so that any variation in the amplitude of the chaotic driving signal degrades the synchronization of the response system to the drive system. In the present work, I show that it is possible to design a response system that reproduces a scaled version of the chaotic driving signal when the drive signal is attenuated or amplified. A simple communications system is demonstrated to show that the type of synchronization described here is useful, and the effects of noise on the communications system are studied.