Yang系统的Hopf分岔分析与控制  

Analysis and Control of Hopf Bifurcation in Yang System

作　　者：闵雪 崔岩[1] MIN Xue;CUI Yan(School of Mechanical and Automotive Engineering,Shanghai University of Engineering Science)

机构地区：[1]上海工程技术大学机械与汽车工程学院

出　　处：《化工自动化及仪表》2018年第12期947-950,共4页Control and Instruments in Chemical Industry

基　　金：国家自然科学基金青年科学基金项目(11604205)

摘　　要：分析Yang系统平衡点Hopf分岔的稳定性及其控制问题。利用中心流形定理和规范型理论得到了分岔解的稳定性指标,推断出系统进入混沌运动是由于它发生了不稳定的分岔而产生的。研究采用线性反馈控制与非线性反馈控制的方法控制该不稳定的Hopf分岔,通过理论计算得出线性反馈控制器仅仅使Hopf分岔得到了延迟控制,分岔的稳定性并没有发生变化,但线性反馈控制器与非线性反馈控制器的共同作用控制了Hopf分岔的稳定性,抑制了系统的混沌行为,系统的稳定性得到增强。通过数值仿真验证了理论分析的正确性。Both stability and control of Hopf bifurcation at Yang system’s equilibrium point was analyzed and having both center manifold theory and normal form theory used to get stability index of bifurcation solution was implemented to conclude that,the system enters into the chaos motion due to unstable Hopf bifurcation.The theoretical calculation indicates that,the linear feedback controller only delays Hopf bifurcation without any change on stability and only combined action of the linear and nonlinear feedback controllers can control stability of Hopf bifurcation and suppress the chaos phenomenon of the system,in this way,the stability of the system is enhanced and the correctness of the theoretical analysis is verified by numerical simulation.

关 键 词：Yang系统 HOPF分岔 非线性动力系统 稳定性 反馈控制 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]