时滞速度反馈对强迫自持系统动力学行为的影响

研究强迫自持振动系统因时滞反馈产生的主共振解及其分岔．通过对强迫非自治系统的时滞反馈控制，得到所要研究的数学模型．讨论对应的线性化系统使平凡平衡态失稳出现周期解的稳定性临界条件．特别关注主共振及分岔．结果表明，稳定的主共振解随着时滞的变化周期性地出现在系统中．同时，也给出了不稳定的主共振关于时滞变化的区域，在理论方面给出了系统出现概周期运动的时滞区域．数据模拟证实了理论结果．

Effects of Time Delayed Velocity Feedbacks on Self-Sustained Oscillator With Excitation

Both the primary resonant solutions and their bifurcations due to time delayed velocity feedbacks used in a self_sustained oscillator with excitation were further investigated.A model was proposed by adding linear and nonlinear time delayed feedbacks to a representative non_autonomous system(with external forcing).The stablity condition of the linearized system at trivial equilibrium was discussed,which leads to a critical stability boundary where periodic solutions may occur.The main attention was focused on bifurcations from the primary resonant solutions.It is found that the stable primary resonant solution may appear periodically in the time delay.Meanwhile,the unstable regions for such solutions are also obtained,predicting the occurrence of quasi_periodic motions.