Application of normal form in chaotic synchronization

Two criteria for converting a chaotic system to a normal form via coordinate transformation are presented. Firstly, it was proved that a chaotic system can be converted to a normal form if and only if there exists a single-input control system which treats the vector field of the chaotic system as drift vector field and can be fully linearized by state feedback. Secondly, near the non-singular point, there always exist some coordinate transformation to perform the converting; and near the singular point, the converting can be found if and only if, at this point, the eigenpolynomial of the Jacobian matrix of the vector field is equal to the minimal polynomial of the same matrix. Moreover, the condition, under which the synchronization between the normal form of the drive system and the Brunovsky canonical form of the response system implies the synchronization between the drive system and the response system, was discussed. Finally, synchronizing two Rossler chaotic systems with difference in two parameters was taken as a concrete example to illustrate the new method.