1.The Special Research Center for Optical Internet & Mobile Information Networks, Ministry Key Laboratory of Broadband Optical Fiber Transmission  & Communication Networks, University of Electronic Science and Technology of China, Chengdu 610054, China; 
2. LATTIS EA no. 4155, INSA, Toulouse University, 135 avenue de Rangueil 31077 Toulouse Cedex 4, France

This paper deals with the model analysis of a chaos generator for secure transmission. In this proposed system discrete value signals and continuous value signals are used together and are interacting one another. The main advantage of this system is that a discrete chaotic map can be implemented in the digital circuit with many parameters, and initial condition can be set with a great accuracy. Also, the problem of periodicity which is always encountered in any fully discrete systems can be avoided. A chaotic behavior study of the system is then provided, in which bifurcation phenomena are explained and chaotic attractors are shown. Finally, an asymptotic chaotic behavior of the proposed system is derived.

This work was supported by the National Science Fund for Distinguished Young Scholars (Grant No. 60725104), the National Basic Research Program of China (Grant No. 2007CB310706), the National High-Tech Research & Development Program of China (Grant Nos. 2007AA01Z246, 2007AA01Z227, 2008AA01Z447, 2008AA011002, 2009AA01Z215), the National Natural Science Foundation of China (Grant Nos. 60672045, 60873263, 60932002, 60932005), the Research Fund for the Doctoral Program of Higher Education (Grant No. 20060614018), the Sichuan Youth Science & Technology Foundation (Grant No. 09ZQ026-032), Youth Foundation of University of Electronic Science and Technology of China (Grant No. L0801010jx0815), and the French Project ANR05RNRT02001 ACSCOM.