Adaptive coupled synchronization among three coupled chaos systems and its application to secure communications

In this paper, the adaptive synchronization method of three coupled identical chaos systems is proposed. New generic criteria of global chaos synchronization and strict theoretical proofs are given. The unidirectional (bidirectional) coupled system will synchronize by adding three adaptive feedback gain equations. As an example, the three Rössler chaotic systems with unidirectional coupling are given to realize the adaptive coupled synchronization; at the same time, the three Lorenz chaotic systems donate the bidirectional coupling adaptive synchronization. This paper also extends the above adaptive synchronization method to secure chaos communications through the method of chaos masking. Based on the three coupled identical Lorenz chaotic systems, a novel method of chaos encryption is proposed, and the basic idea is that after encrypting two times in two transmitters and one receiver, information signal can be recovered exactly at the receiver end. In consideration of interfering random white noise, the results of encoding and decoding are simulated and analyzed for the multistage chaos synchronized system. By analyzing the characteristics of noise, this paper presents a de-noising method using wavelet transform. At last, a secure communications method for high amplitude information signal transmission based on chaotic masking is studied. With the MATLAB, the effects of signal de-noising could be demonstrated.