时滞扰动类Chen系统Hopf分岔分析及控制  

Analysis and control of Hopf bifurcation in Chen system with delayed perturbation

作　　者：丁旭[1] 崔岩 何宏骏 Ding Xu;Cui Yan;He Hongjun(Training Center,Guangdong Voeational Institute of Public Administration.510800.Guangzhou,China;School of Mechanical and Automotive Engineering,Shanghai University of Engineering Science,201620,Shanghai,China)

机构地区：[1]广东行政职业学院实训中心,广州510800 [2]上海工程技术大学机械与汽车工程学院,上海201620

出　　处：《应用力学学报》2020年第3期1239-1244,I0023,共7页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11604205)。

摘　　要：以Chen系统为研究对象,研究其加入扰动项后的动力学特性。分析了时滞扰动Chen系统的平衡点及其稳定性等问题,计算特征根分布及其对应Hopf分岔特征量。根据Hopf分岔定理判断分岔类型及方向,给出分岔发生的条件并运用Matlab仿真验证了当系统经过临界点时会发生Hopf分岔现象。针对时滞扰动带来的Hopf分岔设计线性控制器并将其添加到系统方程中,对其进行滞后控制,仿真结果表明,该控制器使系统在不改变平衡点的前提下,将分岔临界点由0.1609延迟至0.1860,可对扰动引起的Hopf分岔进行有效控制。In this paper,Chen system is taken as the research object to study the dynamic characteristics of the system after adding the disturbance term.The equilibrium points and their stabilities of the Chen system with time-delay disturbance are analyzed briefly,and the characteristic root distribution and its corresponding Hopf bifurcation feature quantity are calculated.According to the Hopf bifurcation theorem,the classification and direction of the bifurcation are judged,and the conditions of bifurcation are given.The Matlab simulation is used to verify that Hopf bifurcation occurs when the system passes the critical point.A linear controller is designed for Hopf bifurcation caused by time-delay disturbance and added to the second equation of equation(12)for hysteresis control.The simulation results show that the controller can effectively control the Hopf bifurcation caused by the disturbance.

关 键 词：CHEN系统 时滞行为 Hopf分岔控制 稳定性 

分 类 号：O193[理学—数学] O415.5[理学—基础数学]