Hopf分岔附近的时滞反馈控制
Delayed Feedback Control near Hopf Bifurcation
摘要：
研究了时滞反馈下泛函微分方程在Hopf分支附近的稳定性。利用平均理论，得到了平衡解稳定的充要条件。结果被用来比较延迟与非延迟反馈，以及离散与分布式延迟。条件获得延迟反馈与部分状态信息可以产生稳定的非延迟反馈是无效的。此外，它表明，如果反馈是稳定的（分别，不稳定），然后离散延迟是局部最稳定的（分别，不稳定）具有相同平均值的延迟分布中的一个。如果考虑关于其均值对称分布的延迟，则结果在全局上也成立。
英文摘要：
The stability of functional differential equations under delayed feedback is investigated near a Hopf bifurcation. Necessary and sufficient conditions are derived for the stability of the equilibrium solution using averaging theory. The results are used to compare delayed versus undelayed feedback, as well as discrete versus distributed delays. Conditions are obtained for which delayed feedback with partial state information can yield stability where undelayed feedback is ineffective. Furthermore, it is shown that if the feedback is stabilizing (respectively, destabilizing), then a discrete delay is locally the most stabilizing (resp., destabilizing) one among delay distributions having the same mean. The result also holds globally if one considers delays that are symmetrically distributed about their mean.
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