Sukow David W., Bleich Michael E., Gauthier Daniel J., Socolar Joshua E. S.
Department of Physics and Center for Nonlinear and Complex Systems, Duke University, P.O. Box 90305, Durham, North Carolina 27708.
Chaos. 1997 Dec;7(4):560-576. doi: 10.1063/1.166256.
We stabilize unstable periodic orbits of a fast diode resonator driven at 10.1 MHz (corresponding to a drive period under 100 ns) using extended time-delay autosynchronization. Stabilization is achieved by feedback of an error signal that is proportional to the difference between the value of a state variable and an infinite series of values of the state variable delayed in time by integral multiples of the period of the orbit. The technique is easy to implement electronically and it has an all-optical counterpart that may be useful for stabilizing the dynamics of fast chaotic lasers. We show that increasing the weights given to temporally distant states enlarges the domain of control and reduces the sensitivity of the domain of control on the propagation delays in the feedback loop. We determine the average time to obtain control as a function of the feedback gain and identify the mechanisms that destabilize the system at the boundaries of the domain of control. A theoretical stability analysis of a model of the diode resonator in the presence of time-delay feedback is in good agreement with the experimental results for the size and shape of the domain of control. (c) 1997 American Institute of Physics.
我们使用扩展时间延迟自同步技术，稳定了一个以10.1兆赫兹驱动的快速二极管谐振器的不稳定周期轨道（对应驱动周期小于100纳秒）。通过反馈一个误差信号来实现稳定，该误差信号与一个状态变量的值和该状态变量按轨道周期整数倍延迟的一系列值之间的差值成正比。该技术在电子上易于实现，并且有一个全光对应物，可能对稳定快速混沌激光器的动力学有用。我们表明，增加赋予时间上较远状态的权重会扩大控制域，并降低控制域对反馈回路中传播延迟的敏感性。我们确定了获得控制的平均时间作为反馈增益的函数，并识别了在控制域边界使系统不稳定的机制。对存在时间延迟反馈的二极管谐振器模型的理论稳定性分析与控制域大小和形状的实验结果非常吻合。(c) 1997美国物理研究所。
