Haken H, Kelso J A, Bunz H
Biol Cybern. 1985;51(5):347-56. doi: 10.1007/BF00336922.
Earlier experimental studies by one of us (Kelso, 1981a, 1984) have shown that abrupt phase transitions occur in human hand movements under the influence of scalar changes in cycling frequency. Beyond a critical frequency the originally prepared out-of-phase, antisymmetric mode is replaced by a symmetrical, in-phase mode involving simultaneous activation of homologous muscle groups. Qualitatively, these phase transitions are analogous to gait shifts in animal locomotion as well as phenomena common to other physical and biological systems in which new "modes" or spatiotemporal patterns arise when the system is parametrically scaled beyond its equilibrium state (Haken, 1983). In this paper a theoretical model, using concepts central to the interdisciplinary field of synergetics and nonlinear oscillator theory, is developed, which reproduces (among other features) the dramatic change in coordinative pattern observed between the hands.
我们其中一人（凯尔索，1981a，1984）早期的实验研究表明，在循环频率的标量变化影响下，人类手部运动会发生突然的相变。超过临界频率后，最初准备的异相、反对称模式会被一种对称的同相模式所取代，该模式涉及同源肌肉群的同时激活。从定性角度来看，这些相变类似于动物运动中的步态转变，以及其他物理和生物系统中的常见现象，即在系统参数缩放超过其平衡状态时会出现新的“模式”或时空模式（哈肯，1983）。在本文中，我们开发了一个理论模型，该模型运用了协同学和非线性振荡器理论这一跨学科领域的核心概念，（除其他特征外）再现了双手之间观察到的协调模式的显著变化。
