Abstract
A relative phase model of four coupled oscillators is used to interpret experiments on the coordination between rhythmically moving human limbs. The pairwise coupling functions in the model are motivated by experiments on two-limb coordination. Stable patterns of coordination between the limbs are represented by fixed points in relative phase coordinates. Four invariant circles exist in the model, each containing two patterns of coordination seen experimentally. The direction of switches between two four-limb patterns on the same circle can be understood in terms of two-limb coordination. Transitions between patterns in the human four-limb system are theoretically interpreted as bifurcations in a nonlinear dynamical system.
Similar content being viewed by others
Literature
Cohen, A. H., P. J. Holmes and R. H. Rand. 1982. The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: A mathematical model.J. math. Biol. 13, 345–369.
Ermentrout, G. B. and N. Kopell. 1984. Frequency plateaus in a chain of weakly coupled oscillators, I.SIAM J. math. Anal. 15 (2), 215–237.
Ermentrout, G. B. and N. Kopell. 1991. Multiple pulse interactions and averaging in systems of coupled neural oscillators.J. math. Biol. 29, 195–217.
Graham, D. 1985 Pattern and control of walking in insects.Adv. Insect Physiol. 18, 31–40.
Haken, H., J. A. S. Kelso and H. Bunz. 1985. A theoretical model of phase transitions in human hand movements.Biol. Cybern. 51, 347–356.
Hirsch, M. W., C. C. Pugh and M. Shub. 1977.Invariant Manifolds. New York: Springer-Verlag.
Jeka, J. J. and J. A. S. Kelso. 1989. Pattern formation in a multistable coordinative system.Soc. Neurosci. Abstr. 15 (1), 605.
Kelso, J. A. S. 1984. Phase transitions and critical behavior in human bimanual coordination.Am. J. Physiol. Regul. Integr. comp. Physiol. 15, R1000-R1004.
Kelso, J. A. S. and J. J. Jeka. 1992. Symmetry breaking dynamics of human multilimb coordination.J. exp. Psychol. Hum. Percept. Perf.,18(3), 645–668.
Kelso, J. A. S., J. D. Delcolle and G. S. Schöner. 1990. Action-perception as a pattern formation process. InAttention and Performance XIII. M. Jeannerod (Ed.), pp. 139–169. Hillsdale, NJ: Erlbaum.
Kelso, J. A. S., J. P. Scholz and G. S. Schöner. 1986. Non-equilibrium phase transitions in coordinated biological motion: Critical fluctuations.Phys. Lett. A118, 279–284.
Kopell, N. 1988. Toward a theory of modelling central pattern generators. InNeural Control of Rhythmic Movements in Vertebrates. A. H. Cohen, S. Rossignol and S. Grillner (Eds), pp. 369–413. New York: John Wiley.
Neu, J. C. 1979. Coupled chemical oscillators.SIAM J. appl. Math. 37 (2), 307–315.
Orlovskii, G. N. and M. L. Shik. 1965. Standard elements of cyclic movement.Biophys. 10, 935–944.
Pearson, K. G. 1976. The control of walking.Sci. Am. 235 (6), 72–86.
Rand, R. H. and P. J. Holmes. 1980. Bifurcation of periodic motions in two weakly coupled van der Pol oscillators.Int. J. non-linear Mech. 15, 387–399.
Schöner, G. S., H. Haken and J. A. S. Kelso. 1986. A stochastic theory of phase transitions in human hand movement.Biol. Cybern. 53, 442–452.
Schöner, G., W. Y. Jiang and J. A. S. Kelso. 1990. A synergetic theory of quadrupedal gaits and gait transitions.J. theor. biol. 142 (3), 359–393.
Shik, M. L. and G. N. Orlovskii. 1965. Co-ordination of the limbs during running of the dog.Biophys. 10, 1148–1159.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Jeka, J.J., Kelso, J.A.S. & Kiemel, T. Pattern switching in human multilimb coordination dynamics. Bltn Mathcal Biology 55, 829–845 (1993). https://doi.org/10.1007/BF02460675
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02460675