Abstract
In this paper a simple adaptive linear feedback control method, based on the invariance principle of differential equations, is proposed for controlling the scaling factor to a desired value. We mathematically prove the synchronizability of the proposed simple adaptive modified projective synchronization control method. Also, we propose a communication scheme based on the adaptive modified projective synchronization of the new chaotic system. Based on the Lyapunov stability theory, an adaptive control law is proposed to make the states of two Lu attractors asymptotically synchronized. Numerical simulations are given to validate the proposed synchronization methods.