储存环自由电子激光的受控Hopf分岔
Controlled Hopf Bifurcation of a storage-ring free-electron laser
摘要：
局部分岔控制是非线性动力系统研究领域中的一个重要课题。我们讨论了存储环自由电子激光物理的背景下，提出了一个新的模型，使系统动力学的分析洞察力内的原始例子。稳定和不稳定的制度之间的过渡，取决于在光学腔中存储的光和循环到环中的电子之间的时间重叠，被发现是一个霍普夫分岔。一个反馈程序的实施和示出提供一个有效的稳定的不稳定的稳态。
英文摘要：
Local bifurcation control is a topic of fundamental importance in the field of nonlinear dynamical systems. We discuss an original example within the context of storage-ring free-electron laser physics by presenting a new model that enables analytical insight into the system dynamics. The transition between the stable and the unstable regimes, depending on the temporal overlapping between the light stored in the optical cavity and the electrons circulating into the ring, is found to be a Hopf bifurcation. A feedback procedure is implemented and shown to provide an effective stabilization of the unstable steady state.
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