分数阶Arneodo混沌系统的自适应同步研究

摘要

选取了三维分数阶Arneodo混沌系统作为研究对象,基于分数阶系统的稳定性定理,对该系统的动力学性质进行分析,发现该系统存在周期态、稳态、混沌态等多种运动状态.通过理论推导和数值计算,得出了分数阶Arneodo系统处于混沌状态时的阶数范围.基于李亚普诺夫稳定性定理和自适应控制理论,通过设计合理的控制器,实现了分数阶Arneodo系统在阶数相同和阶数不同情况下的同步.该结果为混沌系统的同步控制问题及相关研究提供参考.%This paper studied the Arneodo Chaotic System of the three-dimensional fractional order. The dynamic characteristics of the system are made detailed in here through theoretic deduction and numerical simulation and the stability theory of fractional-order system is cited in here.As a result, the range of order is figured out when the system in a chaotic state. It was found that the system has periodic states, steady state, chaotic states. An appropriate control unit is designed based on the adaptive control theory and the stability theory of Lyapunov Function by applying the adaptive technique in the Synchronous Control of the Chaotic System. The complete synchronization is produced when the orders of the system are in the same or different state by applying the adaptive synchronization method. The above result represents important significance to the study on synchronization of chaotic system.