Two observer approaches for synchronization of chaotic Colpitts oscillators: application to secure data transmission

In this paper, a secure data transmission system based on synchronization of two chaotic systems is presented. The transmitter is a chaotic Colpitts oscillator in which the message signal is inserted by inclusion method. Only one of the states of the transmitter is sent to the receiver via a public channel, which is an observer designed to reconstruct all the states of the transmitter, as well as the message. The left inversion problem with observation of complete state is studied in this work. Two types of observer are used: the first one is a sliding mode observer, and the second one is an adaptive observer. Synchronization of the chaotic systems (transmitter - receiver) is obtained and the message signal is recovered by two different methods. Simulation results are presented in order to study the performances of each observer and finally, a comparative study is given.