Optimal synchronization of chaotic systems in noise

Optimal synchronization of two identical chaotic systems coupled in a drive/response manner is considered in the paper. We derive a relationship between the mean square synchronization error and the coupling parameters in the presence of noise. By minimizing the mean square synchronization error with respect to the coupling parameters, an optimal synchronization, which minimizes the synchronization error between the drive and response systems, can be achieved. It is shown that the optimal coupling parameters depend on both the global and local Lyapunov exponents of the chaotic drive system. However, they are independent of the noise power. We apply this approach to design optimal synchronization for various chaotic systems. The optimal design is then applied to chaotic communication and it can recover the information signal efficiently. Simulations show that our theoretical results are in good agreement with the numerical analysis.