分数阶统一混沌系统的修正函数投影同步  

Modified Function Projective Synchronization of the Fractional-order United Chaotic System

作　　者：耿彦峰[1] 王立志[1] 何瑞强[1] 

机构地区：[1]忻州师范学院数学系,山西忻州034000

出　　处：《辽宁工业大学学报（自然科学版）》2017年第3期202-206,共5页Journal of Liaoning University of Technology(Natural Science Edition)

摘　　要：对分数阶统一混沌系统的混沌特性进行了分析。当分数阶取某一定值时,系统表现出混沌性态。通过构造适当的响应系统,设计了一种自适应修正函数投影同步的控制方案。选取合适的控制器以及自适应控制率,利用分数阶微分系统的稳定性理论,证明了分数阶误差系统为渐近稳定,进而得出驱动系统和响应系统最终实现自适应修正函数投影同步,且可以对驱动系统的不确定参数进行估计。最后,利用Adams-Bashforth-Moultom算法,对文中的结论进行数值仿真,其结果说明了该方法的有效性和可行性。For the fractional-order united chaotic system, the chaos behavior is displayed when the fractional-order is used as certain fixed values in this paper. A controlling scheme of adaptive modified function projective synchronization about the united chaotic system is designed by structuring a suitable response system. By means of stability theory of the fractional-order differential systems, it is proved that the zero solution of the error system is asymptotically stable by choosing appropriate controller and adaptive law. Accordingly, it is concluded that master system and response system arrive at adaptive modified function projective synchronization, and the uncertain parameters of master system could be estimated. Finally, an illustrative example with simulations via Adams-Bashforth-Moultom algorithm is used to demonstrate the validity and feasibility of the proposed results.

关 键 词：分数阶 统一混沌系统 修正函数 投影同步 数值仿真 

分 类 号：O193[理学—数学]