Abstract: In this paper, a simple adaptive linear feedback control method is proposed for controlling the scaling factor between two coupled unified chaotic systems to a desired value, based on the invariance principle of differential equations. Under this control strategy, one can arbitrarily select the scaling factor. Numerical simulations are given to support the effectiveness of the proposed method and show the robustness against noise. Furthermore, a secure communication scheme based on the adaptive projective synchronization of unified chaotic systems is presented and numerical simulation shows its feasibility.  

Key words: projective synchronization, adaptive control, unified chaotic system,  secure communication