  In 1985 Haken, Kelso and Bunz proposed a system of coupled nonlinear
oscillators as a model of rhythmic movement patterns in human bimanual
coordination. Since then, the Haken-Kelso-Bunz (HKB) model has become a
modelling paradigm applied extensively in all areas of movement science,
including interpersonal motor coordination. However all previous studies have
followed the line of analysis based on the slow varying amplitude and rotating
wave approximations. These approximations lead to a reduced system comprised of
a single differential equation representing the evolution of the relative phase
of the two coupled oscillators. Here we take a different approach and
systematically investigate the behaviour of the HKB model in the full
four-dimensional state space. We perform detailed numerical bifurcation
analyses and reveal that the HKB model supports previously unreported dynamical
regimes as well as bi-stability between a variety of coordination patterns.
Furthermore, we identify the stability boundaries of distinct coordination
regimes in the model and discuss the applicability of our findings to
interpersonal coordination and other joint-action tasks.
