线性时滞状态反馈下Stuart-Landau系统的多周期解

对一个stuart-landau系统引入时滞状态反馈,研究时滞对非线性系统动力行为的影响。发现时滞可使系统出现周期振动,与无时滞系统不同之处在于有多个周期吸引子共存的现象。从理论上预测由时滞导致的动力学行为,得到周期解的解析形式。随着时滞量的变化,周期解个数及其稳定性发生变化。并通过对比周期解的数值解和解析解,数值验证多周期吸引子共存的现象。这些结果对控制系统的振动和系统同步等有着潜在的应用价值。

Multiple Periodic Solutions in Linear Delayed State Feedback Controlled Stuart-Landau System

By Inducing delayed state feedbacks to a Stuart-Landau system,this paper aim to study the effect of time delay on the dynamics of a classical nonlinear system.It was found that time delay induce periodic oscillations and particularly coexisted multiple periodic attractors,which is totally different from the system without delay.The dynamics of the system time delay induces is predicted analytically,and the analytical form of the periodic solution is also obtained.It follows that the number and stability of the periodic solutions vary with the variation of time delay.The analytical results are in agreement with the numerical ones,which verify the coexisting of the multiple periodic attractors.The results provides some potential applications for the study of oscillation and stabilization of controlled system.