Effects of time-delay in a model of intra- and inter-personal motor coordination

Abstract

Abstract. Motor coordination is an important feature of intra-and inter-personal interactions, and several scenarios -from finger tapping to human-computer interfaces -have been investigated experimentally. In the 1980s, Haken, Kelso and Bunz formulated a coupled nonlinear two-oscillator model, which has been shown to describe many observed aspects of coordination tasks. We present here a bifurcation study of this model, where we consider a delay in the coupling. The delay is shown to have a significant effect on the observed dynamics. In particular, we find a much larger degree of bistablility between in-phase and anti-phase oscillations in the presence of a frequency detuning.

Delayed feedback embedded in perception-action coordination cycles results in anticipation behavior during synchronized rhythmic action: A dynamical systems approach

“…The behavior in Fig 5 is the result of the frequency detuning introduced in Eq (1). Previous studies show that frequency detuning and delayed coupling between synchronizing HKB systems (see the General discussion below for more information about the HKB model) result in anti-phase solutions that are less stable than in-phase activity [32,49]. The behavioral data by Chafe and colleagues [14] supports these observations, since musicians performed the same clapping rhythm in-phase, in an alternating fashion.…”

“…It is noteworthy that other researchers have already built models that could explain and predict human rhythmic coordination behavior by using general physical principles. An important one is the HKB model, which uses a simple equation to explain the possible phase relationships between two coupled oscillatory systems in many contexts, including human intra- and inter-personal synchronization [32]. Because of its focus on relative phase [58], the HKB model is flexible, parsimonious, and a powerful tool to explain and predict periodic human motor behavior [59].…”

“…Although the HKB model has been widely used to explain synchronization behavior, it lacks an explanation of the neurophysiological and biophysical principles that drive synchronization [62]. Some exceptions exist though, since studies have attempted to make the HKB model a more biologically plausible one by explaining how neural connectivity delays affect its behavior [31–32]. While these results are still focused on in-phase and anti-phase phenomena, the added delay allows the HKB model to make predictions about split-brain patients lacking certain modalities of delayed neural cross talk [31] or factors that favor in-phase vs anti-phase stability [32].…”

“…There are parallels between a dynamical system with delayed feedback and the delayed communication between different areas in the sensorimotor system of humans carrying out synchronization. Synchronization requires communication between auditory, premotor and motor brain areas [30–32], which involves delayed transmission of neural information. Moreover, it has been suggested that these delays inherent within the human sensorimotor system may act like ones in coupled dynamical systems with delayed feedback inputs [28,31–32], supporting the strong anticipation theory.…”

“…Synchronization requires communication between auditory, premotor and motor brain areas [30–32], which involves delayed transmission of neural information. Moreover, it has been suggested that these delays inherent within the human sensorimotor system may act like ones in coupled dynamical systems with delayed feedback inputs [28,31–32], supporting the strong anticipation theory. If this holds true, a low-dimensional dynamical systems model could explain anticipation in perception-action coordination.…”