×

Two dimensionless parameters and a mechanical analogue for the HKB model of motor coordination. (English) Zbl 1471.92011

Summary: The widely cited Haken-Kelso-Bunz (HKB) model of motor coordination is used in an enormous range of applications. In this paper, we show analytically that the weakly damped, weakly coupled HKB model of two oscillators depends on only two dimensionless parameters; the ratio of the linear damping coefficient and the linear coupling coefficient and the ratio of the combined nonlinear damping coefficients and the combined nonlinear coupling coefficients. We illustrate our results with a mechanical analogue. We use our analytic results to predict behaviours in arbitrary parameter regimes and show how this led us to explain and extend recent numerical continuation results of the full HKB model. The key finding is that the HKB model contains a significant amount of behaviour in biologically relevant parameter regimes not yet observed in experiments or numerical simulations. This observation has implications for the development of virtual partner interaction and the human dynamic clamp, and potentially for the HKB model itself.

MSC:

92B20 Neural networks for/in biological studies, artificial life and related topics

Software:

AUTO; HomCont
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Alderisio, F.; Bardy, BG; di Bernardo, M., Entrainment and synchronization in networks of Rayleigh-van der Pol oscillators with diffusive and Haken-Kelso-Bunz couplings, Biol Cybern, 110, 2-3, 151-169 (2016) · Zbl 1344.92108
[2] Avitabile, D.; Słowiński, P.; Bardy, BG; Tsaneva-Atanasova, K., Beyond in-phase and anti-phase coordination in a model of joint action, Biol Cybern, 110, 2-3, 201-216 (2016) · Zbl 1345.92093
[3] Banerjee, A.; Jirsa, VK, How do neural connectivity and time delays influence bimanual coordination?, Biol Cybern, 96, 265-278 (2006) · Zbl 1161.92312
[4] Bernstein, NA, The co-ordination and regulation of movements (1967), Oxford: Pergamon Press, Oxford
[5] Bourbousson, J.; Sève, C.; McGarry, T., Space-time coordination dynamics in basketball: Part 1. Intra- and inter-couplings among player dyads, J Sports Sci, 28, 3, 339-347 (2010)
[6] Buchanan, JJ; Ryu, YU, One-to-one and polyrhythmic temporal coordination in bimanual circle tracing, J Motor Behav, 38, 3, 163-184 (2006)
[7] Cass JF (2019) Synchronisation patterns of nonlinearly coupled oscillators. Master’s thesis, Department of Engineering Mathematics, University of Bristol, Sept. 2019
[8] Collins, JJ; Stewart, IN, Coupled nonlinear oscillators and the symmetries of animal gaits, J Nonlin Sci, 3, 1, 349-392 (1993) · Zbl 0808.92012
[9] Doedel EJ, Champneys AR, Fairgrieve TF, Kuznetsov Yu. A, Sandstede B, Wang X (1997) AUTO97: Continuation and bifurcation software for ordinary differential equations (with HomCont). Technical report, Concordia University
[10] Duarte, R.; Araujo, D.; Davids, K.; Travassos, B.; Gazimba, V.; Sampaio, J., Interpersonal coordination tendencies shape 1-vs-1 sub-phase performance outcomes in youth soccer, J Sports Sci, 30, 9, 871-877 (2012)
[11] Dumas, G.; de Guzman, GC; Tognoli, E.; Kelso, JAS, The human dynamic clamp as a paradigm for social interaction, Proc Nat Acad Sci, 111, 35, E3726-E3734 (2014)
[12] Fink, PW; Kelso, JAS; Jirsa, VK; de Guzman, G., Recruitment of degrees of freedom stabilizes coordination, J Exp Psychol: Hum Percept Perform, 26, 2, 671-692 (2000)
[13] Fuchs, A.; Jirsa, VK, The HKB model revisited: how varying the degree of symmetry controls dynamics, Hum Movem Sci, 19, 425-449 (2000)
[14] Fuchs, A.; Jirsa, VK, Coordination: neural, behavioral and social dynamics (2007), New York: Springer, New York
[15] Haken, H.; Kelso, JAS; Bunz, H., A theoretical model of phase-transitions in human hand movements, Biol Cybern, 51, 5, 347-356 (1985) · Zbl 0548.92003
[16] Huys, R.; Perdikis, D.; Jirsa, VK, Functional architectures and structured flows on manifolds: a dynamical framework for motor behavior, Psychol Rev, 121, 3, 302-336 (2014)
[17] Jirsa, VK; Fink, P.; Foo, P.; Kelso, JAS, Parametric stabilization of biological coordination: a theoretical model, J Biol Phys, 26, 85-112 (2000)
[18] Kay, BA; Kelso, JAS; Saltzman, EL; Schöner, G., Space-time behavior of single and bimanual rhythmical movements—data and limit cycle model, J Exp Psychol: Hum Percept Perform, 13, 2, 178-192 (1987)
[19] Kelso, JAS, On the oscillatory basis of movement, Bull Psychonomic Soc, 18, 2, 63 (1981)
[20] Kelso, JAS, Dynamic patterns: the self-organization of brain and behavior (1995), Cambridge: MIT Press, Cambridge
[21] Kelso JAS (2009) Coordination dynamics. Encyclopedia of Complex Syst Sci 1-41
[22] Kelso JAS, de Guzman GC, Reveley C, Tognoli E (2009) Virtual partner interaction (VPI): exploring novel behaviors via coordination dynamics. PloS One 4(6)
[23] Kelso JAS, Del Colle JD, Schöner G (1990) Attention and performance XIII, chapter action-perception as a pattern formation process. In: Jeannerod M (ed) Lawrence Erlbaum Associates, Inc, Hillsdale, pp 139-169
[24] Kelso, JAS; Scholz, JP; Schöner, G., Nonequilibrium phase transitions in coordinated biological motion: critical fluctuations, Phys Lett A, 118, 6, 279-284 (1986)
[25] Leise, T.; Cohen, A., Nonlinear oscillators at our fingertips, Am Math Mon, 114, 1, 14-28 (2007) · Zbl 1334.70040
[26] Nayfeh, AH, Perturbation methods (2008), Hoboken: Wiley, Hoboken
[27] Peper, C.; Lieke, E.; Ridderikhoff, A.; Daffertshofer, A.; Beek, PJ, Explanatory limitations of the HKB model: incentives for a two-tiered model of rhythmic interlimb coordination, Hum Movem Sci, 23, 5, 673-697 (2004)
[28] Schmidt, RC; Carello, C.; Turvey, MT, Phase-transitions and critical fluctuations in the visual coordination of rhythmic movements between people, J Exp Psychol-Hum Percept Perform, 16, 2, 227-247 (1990)
[29] Scholz, JP; Kelso, JAS; Schöner, G., Nonequilibrium phase transitions in coordinated biological motion: critical slowing down and switching time, Phys Lett A, 123, 8, 390-394 (1987)
[30] Schöner, G.; Haken, H.; Kelso, JAS, A stochastic theory of phase transitions in human hand movement, Biol cybern, 53, 4, 247-257 (1986) · Zbl 0587.92030
[31] Słowiński, P.; Al-Ramadhani, S.; Tasaneva-Atanasova, K., Neurologically motivated coupling functions in models of motor coordination, SIAM J Appl Dyn Syst, 19, 208-232 (2020) · Zbl 1446.34092
[32] Słowiński, P.; Tsaneva-Atanasova, K.; Krauskopf, B., Effects of time-delay in a model of intra- and inter-personal motor coordination, Eur Phys J Spec Top, 225, 2591-2600 (2016)
[33] Strogatz, SH, Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering (2018), Boca Raton: CRC Press, Boca Raton
[34] Varlet, M.; Marin, L.; Raffard, S.; Schmidt, RC; Capdevielle, D.; Boulenger, J-P; Del-Monte, J.; Bardy, BG, Impairments of social motor coordination in schizophrenia, PloS One, 7 (2012)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.