Raftery Aaron, Cusumano Joseph, Sternad Dagmar
Department of Kinesiology, Pennsylvania State University, University Park, PA 16802, USA.
Neural Comput. 2008 Jan;20(1):205-26. doi: 10.1162/neco.2008.20.1.205.
The question of how best to model rhythmic movements at self-selected amplitude-frequency combinations, and their variability, is a long-standing issue. This study presents a systematic analysis of a coupled oscillator system that has successfully accounted for the experimental result that humans' preferred oscillation frequencies closely correspond to the linear resonance frequencies of the biomechanical limb systems, a phenomenon known as resonance tuning or frequency scaling. The dynamics of the coupled oscillator model is explored by numerical integration in different areas of its parameter space, where a period doubling route to chaotic dynamics is discovered. It is shown that even in the regions of the parameter space with chaotic solutions, the model still effectively scales to the biomechanical oscillator's natural frequency. Hence, there is a solution providing for frequency scaling in the presence of chaotic variability. The implications of these results for interpreting variability as fundamentally stochastic or chaotic are discussed.
如何以自选择的振幅 - 频率组合最佳地模拟节律性运动及其变异性，这是一个长期存在的问题。本研究对一个耦合振子系统进行了系统分析，该系统成功地解释了一个实验结果，即人类偏好的振荡频率与生物力学肢体系统的线性共振频率密切对应，这一现象被称为共振调谐或频率缩放。通过在其参数空间的不同区域进行数值积分来探索耦合振子模型的动力学，在该过程中发现了通向混沌动力学的倍周期路径。结果表明，即使在具有混沌解的参数空间区域，该模型仍能有效地缩放到生物力学振子的固有频率。因此，存在一种在混沌变异性存在的情况下实现频率缩放的解决方案。讨论了这些结果对于将变异性解释为本质上是随机的还是混沌的意义。
