Neurologically Motivated Coupling Functions in Models of Motor Coordination.

Sohaib Al-Ramadhani,Krasimira Tsaneva-Atanasova,Piotr Słowiński

doi:10.1137/19m1279381

Abstract

We present an analysis of two Haken-Kelso-Bunz (HKB) oscillators coupled by a neurologically motivated function. We study the effect of time delay and weighted self-feedback and mutual feedback on the synchronization behavior of the model. We focus on identifying parameter regimes supporting experimentally observed decrease in oscillation amplitude and loss of anti-phase stability that has inspired the development of the HKB model. We show that a combination of cross-talk and nonlinearity in the coupling, along with physiologically relevant time delay, is able to quantitatively account for both drop in oscillation amplitude and loss of anti-phase stability in a frequency dependent manner. Furthermore, we demonstrate that the transition between discrete and rhythmic movements could be captured by this model. To this end, we carry out theoretical and numerical analysis of the emergence of in-phase and anti-phase oscillations.

Highlights

Intrapersonal and interpersonal motor coordination are active research topics in variety of fields including robotics and human-machine interaction [12, 35], cognitive psychology [47], and neuroscience [55]
Motor coordination has been studied from a dynamical systems point of view for over 30 years since the seminal paper [23] introducing the Haken--Kelso--Bunz (HKB) model, which comprises a system of nonlinearly coupled hybrid Van der Pol--Rayleigh oscillators
We demonstrate that the hybrid oscillator (1.1) with the neurologically motivated coupling (1.3) incorporating time delay accurately captures the empirically observed features of rhythmic movement coordination

Summary

Introduction

Intrapersonal and interpersonal motor coordination are active research topics in variety of fields including robotics and human-machine interaction [12, 35], cognitive psychology [47], and neuroscience [55]. Motor coordination has been studied from a dynamical systems point of view for over 30 years since the seminal paper [23] introducing the Haken--Kelso--Bunz (HKB) model, which comprises a system of nonlinearly coupled hybrid Van der Pol--Rayleigh oscillators. This model qualitatively captures experimental results demonstrating a transition between in-phase and anti-phase dynamics as a result of increase in pacing of driving frequency [22, 30]. The hybrid Van der Pol--Rayleigh oscillator quantitatively accounts for the linear dependence between frequency and amplitude of movement [27, 29].

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