Secure communications via chaotic synchronization in Chua´s circuit and Bonhoeffer-Van der Pol equation: numerical analysis of the errors of the recovered signal

The signal recovered from the first reported experimental secure communication system via chaotic synchronization contains some inevitable noise which degrades the fidelity of the original message. By cascading the output of the receiver in the original system into an identical copy of this receiver, it had be shown by computer experiments that this noise can be significantly reduced. We discuss the heuristic laws governing the errors of the recovered signal which are observed in a new series of very careful computer experiments. This discussion is done comparing these laws to the results obtained using the linear filtering theory. Some discrepancy appears. In order to understand the origin of the discrepancy we consider another simpler model based on the Bonhoeffer-Van der Pol equation where no chaos occurs. In this case both two heuristic laws are in good agreement with the linear filtering theory