Post A A, Peper C E, Daffertshofer A, Beek P J
Institute for Fundamental and Clinical Human Movement Sciences, Faculty of Human Movement Sciences, Vrije Universiteit, Amsterdam, The Netherlands.
Biol Cybern. 2000 Nov;83(5):443-59. doi: 10.1007/s004220000177.
Various stability features of bimanual rhythmic coordination, including phase transitions, have been modeled successfully by means of a one-dimensional equation of motion for relative phase obeying a gradient dynamics, the Haken-Kelso-Bunz model. The present study aimed at assessing pattern stability for stationary performance and estimating the model parameters (a, b, and Q) for the stochastic extension of this model. Estimates of a and b allowed for reconstruction of the potential defining the gradient dynamics. Two coordination patterns between the forearms (in-phase, antiphase) were performed at seven different frequencies. Model parameters were estimated on the basis of an exponential decay parameter describing the relaxation behavior of continuous relative phase following a mechanical perturbation. Variability of relative phase and relaxation time provided measures of pattern stability. Although the predicted inverse relation between pattern stability and movement frequency was observed for the lower tempo conditions, it was absent for the higher tempos, reflecting the influence of task constraints. No statistically significant differences in stability were observed between the two coordination modes, indicating the influence of intention. The reconstructed potential reflected the observed stability features, underscoring the adequacy of the parameter estimations. The relaxation process could not be captured adequately by means of a simple exponential decay function but required an additional oscillatory term. In accordance with previous assumptions, noise strength Q did not vary as a function of movement frequency. However, systematic differences in Q were observed between the two coordination modes. The advantages and (potential) pitfalls of using stationary performance of single patterns to examine the stability features of a bistable potential were discussed.
双手节律性协调的各种稳定性特征，包括相变，已经通过一个服从梯度动力学的相对相位的一维运动方程成功建模，即哈肯-凯尔索-邦兹模型。本研究旨在评估静态表现的模式稳定性，并估计该模型随机扩展的模型参数（a、b和Q）。对a和b的估计使得能够重建定义梯度动力学的势。在前臂之间的两种协调模式（同相、反相）下，以七种不同频率进行实验。基于描述机械扰动后连续相对相位松弛行为的指数衰减参数来估计模型参数。相对相位的变异性和松弛时间提供了模式稳定性的度量。尽管在较低节奏条件下观察到了模式稳定性与运动频率之间预测的反比关系，但在较高节奏下则不存在，这反映了任务约束的影响。在两种协调模式之间未观察到稳定性的统计学显著差异，表明了意图的影响。重建的势反映了观察到的稳定性特征，强调了参数估计的充分性。松弛过程不能通过简单的指数衰减函数充分捕捉，而是需要一个额外的振荡项。与先前的假设一致，噪声强度Q并不随运动频率而变化。然而，在两种协调模式之间观察到了Q的系统差异。讨论了使用单模式的静态表现来检验双稳态势的稳定性特征的优点和（潜在）缺陷。
