The effects of delay on the HKB model of human motor coordination

TL;DR

This paper investigates how delay influences the dynamics of the HKB model for human motor coordination, revealing complex bifurcation phenomena and stability characteristics through combined theoretical and numerical methods.

Contribution

It provides a comprehensive analysis of delay effects on the HKB model, including bifurcation analysis and the discovery of new dynamic behaviors.

Findings

Delay induces bifurcations in the HKB model

Identification of in-phase and anti-phase limit cycles

Discovery of quasi-periodic solutions and phase locking phenomena

Abstract

In this paper, we analyse the celebrated Haken-Kelso-Bunz (HKB) model, describing the dynamics of bimanual coordination, in the presence of delay. We study the linear dynamics, stability, nonlinear behaviour and bifurcations of this model by both theoretical and numerical analysis. We calculate in-phase and anti-phase limit cycles as well as quasi-periodic solutions via double Hopf bifurcation analysis and centre manifold reduction. Moreover, we uncover further details on the global dynamic behaviour by numerical continuation, including the occurrence of limit cycles in phase quadrature and 1-1 locking of quasi-periodic solutions.