河北师范大学学报—

期刊信息

刊名：河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
主办：河北师范大学
ISSN： 1000-5854
CN： 13-1061/N
中国科技核心期刊
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中国高校优秀科技期刊
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分数阶复统一系统的动力学及同步研究

王静

(西安外事学院建筑工程系,西安 710000)
DOI： 10.13763/j.cnki.jhebnu.nse.202402023

Dynamics and Synchronization of a Fractional-order Complex Unified System

WANG Jing

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摘要/Abstract

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.

Abstract：

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

关键词： 分数阶复系统 ; 混沌 ; 分岔 ; 同步

Key words： a fractional-order complex system ; chaos ; bifurcation ; synchronization

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