Modified function projective synchronization of chaotic system

This paper presents a new type synchronization called modified function projective synchronization, where the drive and response systems could be synchronized up to a desired scale function matrix. It is obvious that the unpredictability of the scaling functions can additionally enhance the security of communication. By active control scheme, we take Lorenz system as an example to illustrate above synchronization phenomenon. Furthermore, based on modified function projective synchronization, a scheme for secure communication is investigated in theory. The corresponding numerical simulations are performed to verify and illustrate the analytical results.