ABSTRACT
This chapter deals with the use of the normal forms to analyze observability bifurcations. This concept of normal form was introduced in the context of control theory by W. Kang and Krener. The chapter presents that the normal form in order to analyze observability bifurcations and provides these to the design of chaotic ciphering and deciphering. It provides with this particular application; some basic notions on the system synchronization. An important fact, pointed outs in the 1980s, was the loss of observability due to an inappropriate input. In the unidirectional synchronization case, only stability and observability bifurcation can appear and for bidirectional synchronization stability, observability and controllability bifurcation can appear. To improve the safety of data transmission, a unidirectional synchronization with at least one observability bifurcation is designed. The proposed design requires some specific conditions: observability and observability matching condition.
