In this paper, we study the problem of co-existence of two types of synchronization, complete synchronization and anti-synchronization, in a class of rational discrete chaotic systems. The synchronization scheme derived in this paper is established using new control method and the Lyapunov stability theory. Numerical simulation is presented to demonstrate the effectiveness of the synchronization result derived in this paper.

complete synchronization, anti-synchronization, rational systems, discrete-time, chaos.