Beyond in-phase and anti-phase coordination in a model of joint action.
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 a line of analysis based on slowly varying amplitudes and rotating wave approximations. These approximations lead to a reduced system, consisting of a single differential equation representing the evolution of the relative phase of the two coupled oscillators: the HKB model of the relative phase. Here we take a different approach and systematically investigate the behaviour of the HKB model in the full four-dimensional state space and for general coupling strengths. We perform detailed numerical bifurcation analyses and reveal that the HKB model supports previously unreported dynamical regimes as well as bistability 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.
Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
Daniele
D
Avitabile
Department of Mathematics, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, Devon, EX4 4QF, UK.
Piotr
P
Słowiński
EuroMov, Montpellier University, 700 Avenue du Pic Saint-Loup, 34090, Montpellier, France.|Institut Universitaire de France, Paris, France.
Benoit
B
Bardy
Department of Mathematics, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, Devon, EX4 4QF, UK. K.Tsaneva-Atanasova@exeter.ac.uk.|EPSRC Centre for Predictive Modelling in Healthcare, University of Exeter, Exeter, Devon, EX4 4QF, UK. K.Tsaneva-Atanasova@exeter.ac.uk.
Krasimira
0000-0002-6294-7051
K
Tsaneva-Atanasova
D003491:Cybernetics; D006801:Humans; D007596:Joints / Q000502:physiology*; D008954:Models, Biological; D009068:Movement; D010507:Periodicity
Bifurcation analysis; Coordination regimes; Coupled oscillators; Dynamical system; Numerical continuation; Parameter dependence