Recurrence analysis for the quantification of self-similarity in cyclic movements - Neumann, H. F.; Krug, J. (World Congress of Performance Analysis of Sport VIII, 2008)
Applications of recurrence analysis in human movement studies are rare. Possible reasons may be the expenditure of calculation which complicates the processing of long time series. As seen in the illustrated example it was only possible to process recurrence analysis for single intervals. With the use of this method topology and metrics of race walking were investigated of fractal organisation and dynamics. Even though the trajectories in phase space differed from cycle to cycle, race walking coordination showed local dynamic stability and self-similarity. The found differences at beginning and end of the 30-s-intervals are to interpret to adaptations of velocity. Besides, the mild nonstationarity obtained information of competing strange attractors (e. g. Haken, Kelso & Bunz, 1985; Jordan, Challis & Newell, 2007; Marwan et al., 2007; Richardson, Schmidt & Kay, 2007). In all, motor stability - variability as result of varying initial conditions from cycle to cycle and degrees of freedom control is a dynamic process that follows a chaotic behavior. The results showed both deterministic and stochastic components in this dynamic process. But it is to commend that the stochastic influence was adapted by the motor system in order to keep the topology and reach the aim of the movement in conformance to the competition rules. The apparent stochastic fluctuations suggest following the principle of fractal self-similarity (Briggs & Peat, 2001; Mandelbrot, 1989), for example the intercycle variations of the center of mass ran in self-similar patterns. In all, it is assumed that the motor system adapts different conditions actively (cp. Bernstein, 1988). This assumptation is supported by the fact that, until now, there has been no successful approach to develop gait data out of metric parameters and added stochastic (white) noise that is comparable to real gait data (e. g. Dingwell & Cusumano, 2000; Miller, Stergiou & Kurz, 2006). Nevertheless, in this critical manner, the artificial conditions on the treadmill have to be discussed, too, because velocity is externally fixed (e. g. Dingwell & Cusumano, 2000).