Synchronization and anti-synchronization for chaotic systems

Based on a suitable separation method, combined with the Lyapunov stability and the matrix measure theory, the complete synchronization and anti-synchronization for chaotic systems are investigated. Several sufficient conditions and some necessary and sufficient conditions are obtained respectively. It is proved that these criteria not only are easily verified, but also improve and generalize previously known results, since an adjustable non-singular matrix is given. They are of great significance in the design and applications of synchronization and anti-synchronization of chaotic systems. Two examples are given to show the effectiveness of the proposed method.