Chaotic synchronization by replacing nonlinear terms with signals

A new approach for constructing chaotically synchronizing systems is proposed. The synchronization is achieved via a suitable separation of the chaotic systems and replacement of some nonlinear terms of the response system with driving signals. Since the Lyapunov exponents are not required to calculate, this method is simple and convenient. The Lorenz system is treated as an example and theoretical stability analysis and numerical simulations are also given to validate the proposed technique. Finally, the influence of noise on the synchronization is studied numerically and the results show that the noise has little effect on this kind of synchronization.