A theoretical model of phase transitions in human hand movements

Abstract

Earlier experimental studies by one of us (Kelso, 1981a, 1984) have shown that abrupt phase transitions occur in human hand movements under the influence of scalar changes in cycling frequency. Beyond a critical frequency the originally prepared out-of-phase, antisymmetric mode is replaced by a symmetrical, in-phase mode involving simultaneous activation of homologous muscle groups. Qualitatively, these phase transitions are analogous to gait shifts in animal locomotion as well as phenomena common to other physical and biological systems in which new "modes" or spatiotemporal patterns arise when the system is parametrically scaled beyond its equilibrium state (Haken, 1983). In this paper a theoretical model, using concepts central to the interdisciplinary field of synergetics and nonlinear oscillator theory, is developed, which reproduces (among other features) the dramatic change in coordinative pattern observed between the hands.

Deterministic and stochastic features of rhythmic human movement

“…Also human movement may be characterized as (the result of) a diffusion process, because it can often be captured in the form of common stochastic differential equations, that is, a dynamical system (or differential forms) comprising both deterministic and stochastic components. The unique link between these deterministic and stochastic components and the first two cumulants of the corresponding probability distribution is well documented (Gardiner 2004;Kramers 1940;Moyal 1949;Risken 1989;Stratonovich 1963) and has provided a theoretical framework for understanding the interaction between deterministic and random features (Haken 1983). …”

“…Another example of the usefulness of motor variability can be found in studies of interlimb coordination conducted from a dynamical systems perspective. In this context, variability has been incorporated as random fluctuations to account for phenomena like critical fluctuations and critical slowing down in the vicinity of phase transitions, that is, situations in which a system switches between stable states or attractors, e.g., switches from antiphase to in-phase coordination (Haken et al 1985;Kelso 1984;Post et al 2000;Schöner et al 1986). In relation to the attractor strength, the amount of random fluctuations competes with stability and, thus, determines the flexibility of the system.…”

Challenges for the understanding of the dynamics of social coordination

“…The way this change operates has deep theoretical consequences. Haken et al (1985) assumed that those coordinations obeyed the laws of pattern formation, designed originally for large scale systems in statistical physics. They predicted that the change of pattern corresponded to a phase transition encountered in physics, and thus should operate by a loss of stability of the intended anti-phase pattern.…”

On a Nonlinear Master Equation and the Haken-Kelso-Bunz Model

“…In a far-reaching paper, Haken, Kelso, and Bunz proposed a model to describe multistable rhythmic finger movements [5,25,27,28,30]. In literature, this model is referred to as the HKB model.…”

“…It is nowadays well-documented that for low oscillation frequencies humans can perform bimanual oscillatory index finger movements in only two stable stationary patterns: an in-phase pattern (synchronized activity of homologous muscle groups with zero degree phase-difference ⇒ index fingers move anti-parallel) and an anti-phase pattern (synchronized activity of homologous muscle groups with 180 degrees phase-difference ⇒ index fingers move parallel). For high oscillation frequencies there is only one coordination pattern that can be performed in a stable fashion: the in-phase pattern [5,25,27,28,30]. We assign to the in-phase pattern the stationary phase difference φ st = 0 and to the anti-phase pattern the stationary phase difference φ st = π .…”