Control of projective synchronization in chaotic systems

We show that the scaling factor of projective synchronization in coupled partially linear systems is unpredictable. This gives rise to the difficulty in estimating the state of synchronized dynamics. We therefore propose a control method to manipulate the scaling factor onto any desired value so that the synchronization can be managed in a preferred way. A control law is derived based on the mechanism of projective synchronization of three-dimensional systems and an application is illustrated for the Lorenz system.