Discrete and rhythmic movements — Just a bifurcation apart?

Whether discrete and rhythmic movements result from the same or from separate dynamical structures is yet unclear. We discuss a robust albeit computationally demanding approach to tackle this issue. Our approach capitalizes on conventional time-delay embedding techniques followed by fitting coefficients of a Kramers-Moyal expansion to the so-defined multivariate data. This procedure allows for identifying the generating dynamical systems on basis of possibly non-stationary and noisy signals. We apply this to data from recent experiments in which movement tempo was systematically modified to pinpoint spontaneous switches from discrete to rhythmic movement and back again. It appears that both movement archetypes live in the same phase space but in distinct dynamical regimes.

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