A simple method to synchronize chaotic systems and its application to secure communications

This paper proposes a simple method to synchronize two Lorenz systems with different parameters. One of the Lorenz systems is driven by a variable in the other system. The time series of the driving variable in the drive system and its counterpart in the response system are collected. With the parameters in the response system updated based on skills introduced in this paper, the correlation coefficient and the standard deviation ratio between the time series of the drive and the response system will gradually approach one, which, found by this paper, will cause these two systems to be synchronized. The best set of parameters found for the response system is the one best satisfying the above two conditions. This paper also extends the above idea to secure communications, where the previous driving variable is used to mask an information signal. Using the same strategy as synchronization, these two systems can be synchronized and consequently, the information signal recovered with sufficient precision, as long as the frequency of the information signal is outside the range of the main frequencies of the masking variable and its power level is lower than those of the main frequencies. (c) 2007 Elsevier Ltd. All rights reserved.