Analysis of the Recovered Signal in Synchronized Chua’s Communication System

Abstract

The recovered message signal in the synchronized Chua’s system, which is proposed for secure communications, is analyzed by means of both numerical simulations and analytical methods. The results show that the characteristic of “frequency response” of the system is independent of the amplitude of the input message signal, and the amplitude of the recovered signal is suppressed by the system in the lower frequency range and amplified in the higher frequency range. Specifically, we find that, as the frequency of the input signal increases continuously, there is a band of frequency over which a resonance type of phenomenon occurs in the system whereby the input message’s amplitude is amplified, but the location of this band lies beyond the range of the main spectrum of the chaotic driving signal. The phase difference between input signal and output signal is also obtained. Furthermore based on numerical simulations, the characteristic frequency response of a synchronized Lorenz’s system is given, which also shows a band of resonance in the lower range of frequencies.

Open-loop frequency response for a chaotic masking system

“…[17] agree, in some aspect, with the results obtained in this paper using method, the method in Ref. [17] cannot be extended to deal with other differential equations or iterative systems, but our method used this paper can.…”

“…In Ref. [17] Chen and Pei obtained an analytic solution using the error equations and used it to study the characteristic of frequency response of syn-chronized Chua's circuit. However, it is difficulty to generalize this approach to investigate the frequency response of other chaotic systems.…”