Study On Synchronization Of Fractional-order Chen Chaotic Systems With Applications To Communications

Compared with integer-order chaotic systems theory, the fractional order chaos theory is still in stage of development, many problems remain to be solved. For example, different structures, different dimensions and different order fractional-order chaotic systems synchronization problems need to be studied in-depth, and uncertain parameter fractional-order chaotic systems synchronization and the parameter identification theory research also need to be solved. In this dissertation, the dynamic properties of fractional-order chaotic system are analyzed, and the coupling synchronization, modified projective synchronization and different dimension time-delay synchronization with applications in secure communications are studied. The main contents and contributions are as follows:Firstly, the coupling synchronization of fractional-order chaotic systems with same structure is studied. Based on the stability theory of fractional-order systems, the synchronization of fractional-order Chen coupled chaotic systems is realized using single variable, and the unknown parameters of system can be identified using adaptive rule on parameters. Finally, we apply the above design method to the chaos shift keying secure communications.Secondly, the modified projective synchronization of the fractional-order chaotic systems is studied. Based on the stability theory of fractional order system, the modified projective synchronization of fractional-order chaotic systems with same and different structures is realized using nonlinear control method. The unknown parameters of system are identified using the parametric adaptive rule, and then is applied to the chaotic modulation communication systems.Finally, the synchronization of the time-delay fractional-order chaotic systems with different dimensions is dealt with. Based on the stability theory of fractional order system, the synchronization of time-delay fractional-order chaotic systems is realized, and the unknown parameters of system are identified by the parametric adaptive rule. The correctness of the scheme is verified by simulations.