This paper presents a new compound synchronisation scheme among four hyperchaotic memristor system with incommensurate fractional-order derivatives. First a new controller was designed based on adaptivetechnique to minimise the errors and guarantee compound synchronisation of four fractional-order memristor chaotic systems. According to the suitability of compound synchronisation as a reliable solution for secure communication, we then examined the application of the proposed adaptive compound synchronisation scheme in the presence of noise for secure communication. In addition, the unpredictability and complexity of the drive systems enhance the security of secure communication. The corresponding theoretical analysis and results of simulation validated the effectiveness of the proposed synchronisation scheme using MATLAB.

In this paper, a passive control scheme based on the fractional-order calculus is proposed.We study the modified complex projective synchronisation between two identical fractional-order complex chaotic systems, and its application in the secure communication. The fractional-order complex chaotic Lorenz system is employed to encrypt the emitted signal. In the transmitter module, the information signal is modulated into one parameter of the Lorenz system. It is assumed that the same parameter is unknown in the receiver module. In order to synchronise two systems with different initial conditions, the controllers and an appropriate parameter update rule are designed. Theoretical analysis and numerical simulations show that this method is feasible and robust to some extent in thepresence of channel noise.