Thursday 29 Oct 2015: Dynamics seminar: Numerical Bifurcation Analysis of a model of joint action
Prof. Krasimira Tsaneva-Atanasova - University of Exeter
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.