The Rank Of A Chaotic System And Its Synchronization Study

Chaos is an important branch of nonlinear science, which builds a bridge between determine theory and probability theory. Due to wide applications in secure communi-cation and other fields, chaos synchronization has attracted more and more scholars to research. This thesis is concerned with rank one chaos and synchronization of rank one chaos using a combination method of theoretical derivation and numerical simulation. Main results are as follows:1. The dynamic behavior of the corresponding fractional order chaos systems derived from the integral order rank one chaos which is proposed by Chen and Han in 2009 is researched. Then, based on Barbalat's lemma, the synchronization problem of the integral order rank one chaos which is proposed by Chen and Han in 2009 is discussed using the active control method, adaptive feedback control method and linear control method.2. The dynamic characteristics of the corresponding fractional order chaos sys-tems derived from the integral order rank one chaos which is proposed by Wang and Oksasoglu in 2005 is researched. Based on fractional stability theory, the adaptive control method is adopted to achieved the synchronization of the corresponding frac-tional order chaos systems when the system parametersα,βand b1,b3,βare unknown respectively.