Giesl Peter, Wagner Heiko
Zentrum Mathematik, TU München, Boltzmannstr. 3, 85747 Garching bei München, Germany.
J Math Biol. 2007 Apr;54(4):453-64. doi: 10.1007/s00285-006-0052-8.
This paper provides an explicit Lyapunov function for a general single-joint muscle-skeletal model. Using this Lyapunov function one can determine analytically large subsets of the basin of attraction of an asymptotically stable equilibrium. Besides providing an analytical tool for the analysis of such a system we consider an elbow model and show that the theoretical predictions are in agreement with experimental results. Moreover, we can thus distinguish between regions where the self-stabilizing properties of the muscle-skeletal system guarantee stability and regions where nerval control and reflexes are necessary.
本文为一个通用的单关节肌肉骨骼模型提供了一个显式李雅普诺夫函数。利用这个李雅普诺夫函数，可以通过解析方法确定渐近稳定平衡点吸引域的很大一部分。除了为分析这样一个系统提供一种解析工具外，我们还考虑了一个肘部模型，并表明理论预测与实验结果一致。此外，我们因此可以区分肌肉骨骼系统的自稳定特性保证稳定性的区域和需要神经控制及反射的区域。
