Adaptive synchronisation of diffusionless Lorenz systems and secure communication of digital signals by parameter modulation

Diffusionless Lorenz system of equations is a simplified one-parameter version of the Lorenz system of equations. This system is used here as transmitter and receiver for secure communication. An adaptive control procedure is presented, which causes a rapid convergence of the receiver parameter to the transmitter parameter. This convergence can be used for secure communication of digital signals by parameter modulation. Compared with the Lorenz system, the diffusionless Lorenz system leads to faster communication, smoother parameter adaptation and enhanced security. The proposed scheme is robust with respect to relatively large differences in the delay times for the transmission of three chaotic variables from the master to the slave system. The scheme can be scaled up to allow simultaneous transmission of several signals.