分数阶复统一系统的动力学及同步研究  

Dynamics and Synchronization of a Fractional-order Complex Unified System

作　　者：王静[1] WANG Jing(Department of Civil Engineering,Xi'an International University,Xi'an 710000,China)

机构地区：[1]西安外事学院建筑工程系,西安710000

出　　处：《河北师范大学学报(自然科学版)》2025年第3期262-269,共8页Journal of Hebei Normal University:Natural Science

基　　金：陕西省教育厅一般专项科学研究计划(17JK1019)。

摘　　要：提出了一个带有复状态变量的分数阶统一系统,探讨了系统的动力学行为和同步问题.研究了系统在分数阶阶数相等和不等2种情况下的基本动力学特性,包括不同参数值下的吸引子图、随参数或阶数变化的分岔图.通过分析可得,该系统在参数变化时发生了典型的周期倍分岔和切分岔,所得结果表明该系统具有丰富的动力学行为.同时发现,随着阶数的增大,系统出现混沌的参数阈值变小.基于对该系统动力学的研究,通过设计合适的同步规则和控制器,实现了系统的投影同步;并通过数值模拟验证了所设计的同步规则和控制器的有效性.A fractional-order unified system with complex variables is proposed and studied.Firstly,the dynamical characteristic of the system in the commensurate-order and incommensurate-order cases,including attractors with different values of system parameter and bifurcations diagrams with respect to a parameter or an order,is analyzed.Typical period-doubling and tangent bifurcations are observed.Besides,the critical value of the parameter that chaos appears in the system decreases as the order increases.Furthermore,the synchronization scheme for the fractional-order system is investigated on the basis of the stability theory of fractional-order systems.The synchronization controllers are designed for the system.Simulation results show that the presented scheme and designed controllers are effective.

关 键 词：分数阶复系统 混沌 分岔 同步 

分 类 号：O322[理学—一般力学与力学基础]