RESUMO
Based on advantages of integer and fractional chaotic systems, hybrid chaotic systems and their definitions and some fundamental concepts are proposed, such as hybrid degree (HD), the lowest order (LO) and the total dimension order (TDO). The preliminary properties of hybrid Lorenz systems and hybrid forms of some classic chaotic systems are studied. Then, the relations between HD, LO and TDO with different parameters is investigated in chaotic systems. To be specific, HD is associated with fractional order. It is a directional method to search LO and TDO in chaotic systems. Finally, based on the incommensurate fractional stability theory, we accomplish combination synchronization for three different hybrid order chaotic systems. The simulation results verify the effectiveness of the synchronization controller.
RESUMO
Although complex Lü systems have been considered in many studies, application of the self-time-delay synchronization (STDS) of complex Lü systems in secure speech communications does not appear to have been covered in much of the literature. Therefore, it is meaningful to study the STDS of complex Lü systems and its application in secure speech communication. First, a complex Lü system with double time-delay is introduced and its chaotic characteristics are analyzed. Second, a synchronization controller is designed to achieve STDS. Third, the improved STDS controller is used to design a speech communication scheme based on a complex Lü system. Finally, the effectiveness of the controller and communication scheme are verified by simulation.
