Akamatsu N, Hannaford B, Stark L
Biol Cybern. 1986;53(4):219-27. doi: 10.1007/BF00336992.
A new model based on the theory of dynamical systems is proposed for the intrinsic random or systems is proposed for the intrinsic random or pseudo-random mechanism underlying certain types of muscular tremor. The active length-tension curve of the individual sarcomere, in conjunction with the passive length-tension relation is a map from length to tension with an observed time delay between length change and resulting tension change. The passive length tension relation is assumed to instantaneously relate this tension change back to a change in length. The stability properties of this iterated interval map are investigated by means of computer simulation and computation of the Lyapunov exponent and the bifurcation tree. The resulting analysis is related to experimental tremor data in the literature in terms of period doubling, bifurcation points, and "chaotic" behavior. The model appears to have its most fruitful application in understanding the insect type and isometric mammalian types of tremor.
基于动力系统理论提出了一种新模型，用于解释某些类型肌肉震颤背后的内在随机或伪随机机制。单个肌节的主动长度-张力曲线，结合被动长度-张力关系，是一个从长度到张力的映射，在长度变化和由此产生的张力变化之间存在观测到的时间延迟。假定被动长度-张力关系能将这种张力变化即时地反馈为长度变化。通过计算机模拟以及李雅普诺夫指数和分岔树的计算，研究了这种迭代区间映射的稳定性特性。根据倍周期、分岔点和“混沌”行为，将所得分析结果与文献中的实验性震颤数据相关联。该模型在理解昆虫型和等长哺乳动物型震颤方面似乎有最富有成效的应用。
