时滞反馈下分数阶Rayleigh系统的稳定性分析  

Stability analysis of a fractional-order Rayleigh system with time-delayed feedback

作　　者：陈聚峰[1,2] 申永军 张静[4] 李向红 王晓娜[5] CHEN Jufeng;SHEN Yongjun;ZHANG Jing;LI Xianghong;WANG Xiaona(State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;Department of Mathematics and Physics,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;Department of Mechanical Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;Department of Basic Teaching,Shijiazhuang Posts and Telecommunications Technical College,Shijiazhuang 050021,China;Department of Mechanical and Electrical Engineering,Hebei Vocational College of Rail Transportation,Shijiazhuang 050021,China)

机构地区：[1]石家庄铁道大学省部共建交通工程结构力学行为与系统安全国家重点实验室,石家庄050043 [2]石家庄铁道大学数理系,石家庄050043 [3]石家庄铁道大学机械工程学院,石家庄050043 [4]石家庄邮电职业技术学院基础部,石家庄050021 [5]河北轨道运输职业技术学院机电工程系,石家庄050021

出　　处：《振动与冲击》2023年第2期1-6,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金(U1934201;11772206;12172233);国家重点实验室自主课题项目(ZZ2021-14)。

摘　　要：该研究主要探讨了时滞反馈下分数阶Rayleigh系统的稳定性和Hopf分岔发生的条件。首先,得到具有线性速度反馈的分数阶Rayleigh系统的平衡点渐近稳定的充要条件,发现它不仅与反馈增益有关,还与分数阶阶次有关。其次,以时滞作为分岔参数,对具有线性时滞速度反馈的分数阶Rayleigh系统进行稳定性分析。在一定条件下,计算出时滞的临界值,当时滞参数小于该值时,平衡点是稳定的;当时滞参数大于该值时,平衡点是不稳定的。进而,得到Hopf分岔发生的条件。最后,选取三组系统参数进行数值模拟,验证了所得理论结果的正确性。The stability and existence conditions of the Hopf bifurcation of a commensurate Rayleigh system with time-delayed feedback were studied.The necessary and sufficient conditions of the asymptotic stability of the equilibrium point of the fractional-order Rayleigh system with linear velocity feedback were obtained,and it is found that the conditions are not only related to the feedback gain,but also to the fractional order.Regarding the time delay as a bifurcation parameter,the stability of the commensurate fractional-order Rayleigh system with time-delayed feedback was investigated based on the characteristic equation.Under some conditions,the critical value of time delay was calculated・The equilibrium point is stable when the parameter is less than the critical value and will be unstable if the parameter is greater than it.Moreover,the conditions for the occurrence of Hopf bifurcation were obtained.Choosing three typical system parameters,some numerical simulations were carried out to verify the correctness of the obtained theoretical results.

关 键 词：Rayleigh系统 稳定性 时滞 HOPF分岔 

分 类 号：O193[理学—数学] O322[理学—基础数学]