Sieber J, Gonzalez-Buelga A, Neild S A, Wagg D J, Krauskopf B
School of Engineering, University of Aberdeen, Kings College, Aberdeen, AB24 3UE, United Kingdom.
Phys Rev Lett. 2008 Jun 20;100(24):244101. doi: 10.1103/PhysRevLett.100.244101. Epub 2008 Jun 19.
We present a continuation method that enables one to track or continue branches of periodic orbits directly in an experiment when a parameter is changed. A control-based setup in combination with Newton iterations ensures that the periodic orbit can be continued even when it is unstable. This is demonstrated with the continuation of initially stable rotations of a vertically forced pendulum experiment through a fold bifurcation to find the unstable part of the branch.
我们提出了一种连续方法，当一个参数发生变化时，该方法能使人们在实验中直接追踪或延续周期轨道的分支。基于控制的设置与牛顿迭代相结合，确保即使周期轨道不稳定也能延续。通过垂直强迫摆实验中初始稳定旋转的延续，经过折叠分岔来找到分支的不稳定部分，证明了这一点。
