The excitator as a minimal model for the coordination dynamics of discrete and rhythmic movement generation

Journal of Motor Behavior

Volumn 37, Issue 1, 2005, Pages 35-51

  Jirsa, Viktor K ^a   Kelso, J A Scott ^a  

^a FLORIDA ATLANTIC UNIVERSITY   (United States)

Author keywords

Convergence; Coupling; Divergence; False start

Indexed keywords

ARTICLE; BIOMECHANICS; LIMB MOVEMENT; MATHEMATICAL ANALYSIS; MODEL; MOTOR COORDINATION; RHYTHM; SIMULATION;

HUMANS; MODELS, THEORETICAL; MOVEMENT; PERIODICITY; PSYCHOMOTOR PERFORMANCE;

EID: 11144344479     PISSN: 00222895     EISSN: None     Source Type: Journal    
DOI: 10.3200/JMBR.37.1.35-51     Document Type: Article

References (68)

1. Amari, S. (1977). Dynamics of pattern formation in lateral-inhibition type neural fields. Biological Cybernetics, 27, 77-87.
2. Balasubramaniam, R., & Feldman, A. G. (2004). Guiding movements without redundancy problems. In V. K. Jirsa & J. A. S. Kelso (Eds.), Coordination dynamics: Issues and trends (pp. 155-176). New York: Springer.
3. Beek, P. J., Peper, C. E., & Daffertshofer, A. (2002). Modeling rhythmic interlimb coordination: Beyond the Haken-Kelso-Bunz model. Brain and Cognition, 48(1), 149-165.
4. Campbell, S. R., & Wang, D. (1998). Relaxation oscillators with time delay coupling. Physica D, 111(1-4), 151-178.
5. Collet, C. (1999). Strategic aspects of reaction time in world-class sprinters. Perceptual and Motor Skills, 88(1), 65-75.
6. Croot, K., Hodges, J. R., Xuereb, J., & Patterson, K. (2000). Phonological and articulatory impairment in Alzheimer's disease: A case series. Brain and Language, 75, 277-309.
7. Daffertshofer, A., Peper, C. E., & Beek, P. J. (2004). Stabilization of bimanual coordination due to active inhibition-Evidence from phase transitions. (Manuscript submitted for publication).
8. Feldman, A. G. (198Oa). Superposition of motor programs. I. Rhythmic forearm movements in man. Neuroscience, 5, 81-90.
9. Feldman, A. G. (1980b). Superposition of motor programs. II. Rapid flexion of forearm in man. Neuroscience, 5, 91-95.
10. FitzHugh, R. (1961). Impulses and physiological states in theoretical models of nerve membrane. Biophysical Journal, 1, 445-466.
11. Freeman, W. J. (1992). Tutorial on neurobiology: From single neurons to brain chaos. International Journal of Bifurcation and Chaos, 2, 451-482.
12. Fuchs, A., & Jirsa, V. K. (2000). The HKB model revisited: How varying the degree of symmetry controls dynamics. Human Movement Science, 19(4), 425-449.
13. Fuchs, A., Jirsa, V. K., & Kelso, J. A. S. (2000). Theory of the relation between human brain activity (MEG) and hand movements. Neuroimage, 11, 359-369.
14. Fuchs, A., Kelso, J. A. S., & Haken, H. (1992). Phase transitions in the human brain: Spatial mode dynamics. International Journal of Bifurcation and Chaos, 2, 917-939.
15. Fuchs, A., Mayville, J. M., Cheyne, D., Weinberg, H., Deecke, L., & Kelso, J. A. S. (2000). Spatiotemporal analysis of neuromagnetic events underlying the emergence of coordinative instabilities. Neuroimage, 12, 71-84.
16. Gonzalez, D. L., & Piro, O. (1987). Global bifurcations and phase portrait of an analytically solvable nonlinear oscillator: Relaxation oscillations and saddle-node collisions. Physical Review A, 36, 4402-4410.
17. Grossberg, S., Pribe, C., & Cohen, M. A. (1997). Neural control of interlimb oscillations. I. Human bimanual coordination. Biological Cybernetics, 77, 131-140.
18. Guckenheimer, J., & Holmes, P. (1983). Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. New York: Springer.
19. Hackley, S. A., & Valle-Inclán (1998). Automatic alerting does not speed late motoric processes in a reaction-time task. Nature, 391, 786-788.
20. Haken, H. (1983). Synergetics. An Introduction (3rd ed.). New York: Springer.
21. Haken, H. (1996). Principles of brain functioning. New York: Springer.
22. Haken, H. (2002). Brain dynamics. New York: Springer.
23. Haken, H., Kelso, J. A. S., & Bunz, H. (1985). A theoretical model of phase transitions in human hand movements. Biological Cybernetics, 51, 347-356.
24. Hindmarsh, J. L., & Rose, R. M. (1982). A model of the nerve impulse using two first-order differential equations. Nature, 296(5853), 162-164.
25. Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology, 117, 500-544.
26. Jirsa, V. K. (2004). Information processing in brain and behavior displayed in large-scale topographies such as EEG and MEG. International Journal of Bifurcation and Chaos, 14(2), 679-692.
27. Jirsa, V. K., Friedrich, R., & Haken, H. (1995). Reconstruction of the spatiotemporal dynamics of a human magnetoencephalogram. Physica D, 89, 100-122.
28. Jirsa, V. K., Friedrich, R., Haken, H., & Kelso, J. A. S. (1994). A theoretical model of phase transitions in the human brain. Biological Cybernetics, 71, 27-35.
29. Jirsa, V. K., Fuchs, A., & Kelso, J. A. S. (1998). Connecting cortical and behavioral dynamics: Bimanual coordination. Neural Computation, 10, 2019-2045.
30. Jirsa, V. K., & Haken, H. (1996). Field theory of electromagnetic brain activity. Physical Review Letters, 77, 960-963.
31. Jirsa, V. K., & Haken, H. (1997). A derivation of a macroscopic field theory of the brain from the quasi-microscopic neural dynamics. Physica D, 99, 503-526.
32. Jirsa, V. K., & Kelso, J. A. S. (2000). Spatiotemporal pattern formation in neural systems with heterogeneous connection topologies. Physical Review E, 62, 8462-8465.
33. Jirsa, V. K., & Kelso, J. A. S. (2004). Coordination dynamics: Issues and trends. New York: Springer.
34. Kay, P. A., Kelso, J. A. S., Saltzmann, E. L., & Schöner, G. (1987). Space-time behavior of single and bimanual rhythmical movements: Data and limit cycle model. Journal of Experimental Psychology, 13, 178-192.
35. Kelso, J. A. S. (1977). Motor control mechanisms underlying human movement reproduction. Journal of Experimental Psychology: Human Perception and Performance, 3, 529-543.
36. Kelso, J. A. S. (1981). On the oscillatory basis of movement. Bulletin of the Psychonomic Society, 18, 63.
37. Kelso, J. A. S. (1995). Dynamic patterns. The self-organization of brain and behavior. Cambridge, MA: MIT Press.
38. Kelso, J. A. S. (2002). The complementary nature of coordination dynamics: Self-organization and the origins of agency. Journal of Nonlinear Phenomena in Complex Systems, 5, 364-371.
39. Kelso, J. A. S., Bressler, S. L., Buchanan, S., DeGuzman, G. C., Ding, M., Fuchs, A., et al. (1992). A phase transition in human brain and behavior. Physics Letters A, 169, 134-144.
40. Kelso, J. A. S., DelColle, J. D., & Schöner, G. (1990). Action-perception as a pattern formation process. In M. Jeannerod (Ed.), Attention and performance Kill (pp. 136-169). Hillsdale, NJ: Erlbaum.
41. Kelso, J. A. S., Fuchs, A., Lancaster, R., Holroyd, T., Cheyne, D., & Weinberg, H. (1998). Dynamic cortical activity in the human brain reveals motor equivalence. Nature, 23, 814-818.
42. Kelso, J. A. S., & Holt, K. G. (1980). Exploring a vibratory systems-analysis of human movement production. Journal of Neurophysiology, 43(5), 1183-1196.
43. Kelso, J. A. S., Putnam, C. A., & Goodman, D. (1983). On the space-time structure of human interlimb coordination. Quarterly Journal of Experimental Psychology, 35A, 347-375.
44. Kelso, J. A. S., Southard, D., & Goodman, D. (1979). On the coordination of two-handed movements. Journal of Experimental Psychology: Human Perception and Performance, 5, 229-238.
45. Kuramoto, Y. (1984). Chemical oscillations, waves, and turbulence. New York: Springer.
46. Mayville, J. M., Jantzen, K. J., Fuchs, A., Steinberg, F. L., & Kelso, J. A. S. (2002). Cortical and subcortical networks underlying syncopated and synchronized coordination revealed using fMRI. Human Brain Mapping, 17, 214-229.
47. Meyer-Lindenberg, A., Ziemann, U., Hajak, G., Cohen, L., & Berman, K. F. (2002). Transitions between dynamical states of differing stability in the human brain. Proceedings of the National Academy of Sciences, 99(17), 10948-10953.
48. Murray, J. D. (1993). Mathematical biology. New York: Springer.
49. Nagashino, H., & Kelso, J. A. S. (1992). Phase transitions in oscillatory neural networks. Science of Artificial Neural Networks, International Society for Optical Engineering, 1710, 278-297.
50. Nunez, P. L. (1974). The brain wave equation: A model for the EEG. Mathematical Biosciences, 21, 279-297.
51. Nunez, P. L. (1995). Neocortical dynamics and human EEC rhythms. Oxford, England: Oxford University Press.
52. Peper, C. L. E., & Beek, P. J. (1998). Are frequency-induced transitions in rhythmic coordination mediated by a drop in amplitude? Biological Cybernetics, 79(4), 291-300.
53. Perko, L. (1991). Differential equations and dynamical systems. New York: Springer.
54. Polit, A., & Bizzi, E. (1978). Processes controlling arm movements in monkeys. Science, 201, 1235-1237.
55. Polit, A., & Bizzi, E. (1979). Characteristics of motor programs underlying arm movements in monkeys. Journal of Neurophysiology, 42, 183-194.
56. Postma, A. (2000). Detection of errors during speech production: A review of speech monitoring models. Cognition, 77, 97-131.
57. Pribe, C., Grossberg, S., & Cohen, M. A. (1997). Neural control of interlimb oscillations. II. Biped and quadruped gaits and bifurcations. Biological Cybernetics, 77, 141-152.
58. Robinson, P. A., Rennie, C. A., & Wright, J. J. (1997). Propagation and stability of waves of electrical activity in the cerebral cortex. Physical Review E, 56, 826.
59. Schmidt, R. A., & Gordon, G. B. (1977). Errors in motor responding, "rapid" corrections, and false anticipations. Journal of Motor Behavior, 9, 101-111.
60. Schmidt, R. A., & McGown, C. (1980). Terminal accuracy of unexpectedly loaded rapid movements. Evidence for a mass-spring mechanism in programming. Journal of Motor Behavior, 12, 149-161.
61. Schöner, G. (1990). A dynamic theory of coordination of discrete movement. Biological Cybernetics, 63, 257-270.
62. Schöner, G., Haken, H., & Kelso, J. A. S. (1986). A stochastic theory of phase transitions in human hand movement. Biological Cybernetics, 53, 247-257.
63. Sternad, D., Dean, W. J., & Schaal, S. (2000). Interaction of rhythmic and discrete pattern generators in single-joint movements. Human Movement Science, 19(4), 627-664.
64. Strogatz, S. H. (1994). Nonlinear dynamics and chaos. Reading, MA: Addison-Wesley.
65. Wilson, H. R., & Cowan, J. D. (1972). Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical Journal, 12, 1-24.
66. Wilson, H. R., & Cowan, J. D. (1973). A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik, 13, 55-80.
67. Wing, A. M., & Kristofferson, A. B. (1973). Response delays and the timing of discrete motor responses. Perception and Psychophysics, 14, 5-12.
68. Wright, J. J., & Liley, D. T. J. (1996). Dynamics of the brain at global and microscopic scales: Neural networks and the EEG. Behavioral Brain Sciences, 19, 285.