Eisenhammer T, Hübler A, Packard N, Kelso J A
Physics Department, University of Illinois, Urbana 61801.
Biol Cybern. 1991;65(2):107-12. doi: 10.1007/BF00202385.
Recently some methods have been presented to extract ordinary differential equations (ODE) directly from an experimental time series. Here, we introduce a new method to find an ODE which models both the short time and the long time dynamics. The experimental data are represented in a state space and the corresponding flow vectors are approximated by polynomials of the state vector components. We apply these methods both to simulated data and experimental data from human limb movements, which like many other biological systems can exhibit limit cycle dynamics. In systems with only one oscillator there is excellent agreement between the limit cycling displayed by the experimental system and the reconstructed model, even if the data are very noisy. Furthermore, we study systems of two coupled limit cycle oscillators. There, a reconstruction was only successful for data with a sufficiently long transient trajectory and relatively low noise level.
最近，一些方法已被提出用于直接从实验时间序列中提取常微分方程（ODE）。在此，我们介绍一种新方法来找到一个既能模拟短期动态又能模拟长期动态的ODE。实验数据在状态空间中表示，相应的流向量由状态向量分量的多项式近似。我们将这些方法应用于模拟数据以及来自人类肢体运动的实验数据，人类肢体运动与许多其他生物系统一样，能够展现极限环动力学。在只有一个振荡器的系统中，即使数据噪声很大，实验系统显示的极限环与重建模型之间也有很好的一致性。此外，我们研究了两个耦合极限环振荡器的系统。在那里，只有当数据具有足够长的瞬态轨迹且噪声水平相对较低时，重建才会成功。
