Evaluation of coordination hysteresis in a multidimensional movement task with continuous relative phase and Self-Organizing Maps

Hysteresis in the coordination of movement can be described in the language of coordination dynamics as an asymmetrical response of a system's order parameter with respect to opposite changes in a control parameter. For movement tasks involving a large number of active degrees-of-freedom, the order parameter can be modelled with a pattern recognition approach like Self-Organizing Maps (SOM). This study explored this method in a rope-skipping task, which involves the coordinated oscillation of several segments in the lower and upper limb and trunk and we compared the results to a classical order parameter like continuous relative phase. Five rope skippers completed a task which involved 30 s continuous forward rope-skipping during which the frequency (set by a metronome) increased linearly, immediately followed by 30 s during which the frequency decreased linearly. CRP was analyzed with statistical parametric mapping and a hysteresis measure for the SOM was calculated based on inter-trial variability. Both the CRP and the SOMs showed that the coordination patterns changed differently during the two conditions, signifying hysteresis. While the CRP captures only the relative coordination of two segments, the SOM is able to accommodate the whole-body multidimensional coordination. Hysteresis is often used as proxy for higher-order information about the movement system. While the low sample size in this study does not allow us to generalize the results, the present methodology can be used in further studies to advance our theoretical understanding of dynamical systems in complex whole-body movements.