Free Access
Math. Model. Nat. Phenom.
Volume 6, Number 6, 2011
Biomathematics Education
Page(s) 260 - 277
Section Continuous Modeling
Published online 05 October 2011
  1. D. Acheson. From Calculus to Chaos: An introduction to dynamics. Oxford University Press, New York (1998). [Google Scholar]
  2. A. Armenti, Jr., editor. The Physics of Sports. American Institute of Physics, New York (1992). [Google Scholar]
  3. Y. Asai, Y. Tasaka, K. Nomura, T. Nomura, M. Casidio, P. Morasso A model of postural control in quiet standing: Robust compensation of delay–induced instability using intermittent activation of feedback control. PLoS ONE 4 (2009), e6169. [Google Scholar]
  4. G. L. Baker, J. A. Blackburn. The pendulum: a case study in physics. Oxford University Press, New York, 2005. [Google Scholar]
  5. H. C. Berg. Random walks in biology. Princeton University Press, New Jersey (1993). [Google Scholar]
  6. A. Bottaro, Y. Yasutake, T. Nomura, M. Casidio, P. Morasso. Bounded stability of the quite standing position: An intermittent control model. Human Movement Science 27 (2008), 473–495. [CrossRef] [PubMed] [Google Scholar]
  7. R. Bormann, J. L. Cabrera, J. G. Milton, C. W. Eurich. Visuomotor tracking on a computer screen: An experimental paradigm to study dynamics of motor control. Neurocomputing 58–60 (2004), 517-523. [Google Scholar]
  8. J. Boulet, R. Balasubramiam, A. Daffertshofer, A. Longtin. Stochastic two-delay differential model of delayed visual feedback effects on postural dynamics. Phil. Trans. Roy. Soc. A 368 (2010): 423-438. [CrossRef] [Google Scholar]
  9. J. L. Cabrera, J. G. Milton. On–off intermittency in a human balancing task. Phys. Rev. Lett. 89 (2002), 158702. [CrossRef] [PubMed] [Google Scholar]
  10. J. L. Cabrera, J. G. Milton. Human stick balancing: Tuning Lévy flights to improve balance control. CHAOS 14 (2004): 691. [Google Scholar]
  11. J. L. Cabrera, R. Bormann, C. Eurich, T. Ohira, J. Milton. State–dependent noise and human balance control. Fluct. Noise Lett. 4 (2004), L107-L118. [CrossRef] [Google Scholar]
  12. S. A. Campbell, S. Crawford, K. Morris. Friction and the inverted stabilization problem. J. Dyn. Syst. Meas. Control. 130 (2008), 054502. [Google Scholar]
  13. J. J. Chiel, R. D. Beer. The brain has a body: adaptive behavior emerges from interactions of nervous system, body and environment. TINS 20 (1997), 553–557. [Google Scholar]
  14. T. Cluff, R. Balasubramania R.. Motor learning characterized by changing Lévy distributions. PLoS One 4 (2009): e5998. [Google Scholar]
  15. V. de Silva, J. B. Tenenbaum, J. C. Langford. A global geometric framework for nonlinear dimensionality reduction. Science 290 (2000), 2319–2323. [Google Scholar]
  16. T. M. H. Dijkstra, H. Katsumata, D. Sternad. The dialogue between data and model: passive stability and relaxation behavior in a ball bouncing task. Nonlinear Studies 11 (2004), 319–344. [MathSciNet] [Google Scholar]
  17. B. Ermentrout. Simulating, Analyzing, and Animating Dynamical Systems. SIAM, Philadelphia (2002). [Google Scholar]
  18. C. W. Eurich, J. G. Milton JG. Noise-induced transitions in human postural sway. Phys. Rev. E 54 (1996): 6681-6684. [Google Scholar]
  19. C. W. Eurich, K. Pawelzik. Optimal control yields power laws. In Artificial Neural Networks: Formal Models and Their Applications, Springer Lecture Notes in Computer Science Vol. 3697, edited by W. Duch, J. Kacprzyk, E. Oja and S. Zadronzny (Springer–Verlag, Berlin, 2005), pp. 365–370. [Google Scholar]
  20. P. Foo, J. A. S. Kelso, G. D. de Guzman. Functional stabilization of fixed points: Human pole balancing using time to balance information. J. Exp. Psychol. Hum. Percept. Perform. 26 (2000), 1281-1297. [CrossRef] [PubMed] [Google Scholar]
  21. J. Guckenheimer. A robust hybrid stabilization strategy for equilibria. IEEE Trans. Automatic Control 40 (1995), 321–326. [CrossRef] [Google Scholar]
  22. T. Insperger. Stick balancing with reflex delay in case of parametric forcing. Commun. Nonlinear Sci. Numer. Simulat. 16 (2011), 2160–2168. [CrossRef] [Google Scholar]
  23. A. Kamimura, T. Ohira. Group chase and escape. New J. Physics 12 (2010), 053013. [CrossRef] [Google Scholar]
  24. T. A. Kuiken, L. A. Miller, R. D. Lipschutz, B. A. Lock, K. Stubblefield, P. D. Marasso, P. Zhou, G. A. Dumanian. Targeted reinnervation for enhanced prosthetic arm function in a woman with a proximal amputation: a case study. Lancet 369 (2007), 371–380. [CrossRef] [PubMed] [Google Scholar]
  25. A. D. Kuo. The six determinants of gait and the inverted pendulum analogy: A dynamic walking perspective. Hum. Mov. Sci. 26 (2007), 617–656. [CrossRef] [PubMed] [Google Scholar]
  26. S. S. Lafon. Diffusion Maps and Geometric Harmonics. PhD thesis, Yale University, 2004. [Google Scholar]
  27. M. Landry, S. A. Campbell, K. Morris, C. O. Aguilar. Dynamics of an inverted pendulum with delayed feedback control. SIAM J. Appl. Dyn. Sys. 4 (2005), 333–351. [CrossRef] [Google Scholar]
  28. D. B. Lockhart, L. H. Ting. Optimal sensorimotor transformations for balance. Nat. Neurosci. 10 (2007), 1329–1336. [CrossRef] [PubMed] [Google Scholar]
  29. I. D. Loram, M. Lackie. Human balancing of an inverted pendulum: position control by small, ballistic–like, throw and catch movements. J. Physiol. (London) 540 (2002), 1111-1124. [CrossRef] [PubMed] [Google Scholar]
  30. I. D. Loram, C. N. Maganaris, M. Lakie. Human postural sway results from frequent, ballistic bias impulses by soleus and gastrocnemius. J. Physiol. (London) 564 (2005), 295-311. [CrossRef] [PubMed] [Google Scholar]
  31. J. Maynard Smith. Mathematical Ideas in Biology. Cambridge University Press, New York (1968). [Google Scholar]
  32. T. A. McMahon. Muscles, Reflexes and Locomotion. Princeton University Press, New Jersey (1984). [Google Scholar]
  33. B. Mehta, S. Schaal. Forwards models in visuomotor control. J. Neurophysiol. 88 (2002), 942–953. [PubMed] [Google Scholar]
  34. J. G. Milton, S. S. Small, A. Solodkin. On the road to automatic: Dynamic aspects in the development of expertise. J. Clin. Neurophysiol. 21 (2004), 134–143. [Google Scholar]
  35. J. G. Milton, J. L. Cabrera, T. Ohira. Unstable dynamical systems: Delays, noise and control. Europhys. Lett. 83 (2008), 48001. [Google Scholar]
  36. J. G. Milton, T. Ohira, J. L. Cabrera, R. M. Fraiser, J. B. Gyorffy, F. K. Ruiz, M. A. Strauss, E. C. Balch, P. J. Marin, J. L. Alexander. Balancing with vibration: A prelude for “drift and act” balance control. PLOS One 4 (2009), e7427. [Google Scholar]
  37. J. Milton, J. L. Cabrera, T. Ohira, S. Tajima, Y. Tonosaki, C. W. Eurich, S. A. Campbell. The time–delayed inverted pendulum: Implications for human balance control. Chaos 19 (2009), 026110. [Google Scholar]
  38. J. Milton, J. L. Townsend, M. A. King, T. Ohira. Balancing with positive feedback: the case for discontinuous control. Phil. Trans. Roy. Soc. A 367 (2009), 1181-1193. [CrossRef] [Google Scholar]
  39. J. Milton, J. Gyorffy, J. L. Cabrera, T. Ohira. Amplitude control of human postural sway using Achilles tendon vibration. 16th US National Congress of Theoretical and Applied Mechanics (2010). State College, PA (USNCTAM2010–791). [Google Scholar]
  40. J. G. Milton, A. E. Radunskaya, A. H. Lee, L. G. de Pillis, D. F. Bartlett. Team research at the biology–mathematics interface: Project management perspectives. CBE–Life Sciences Education 9 (2010), 316-322. [Google Scholar]
  41. J. Milton, P. Naik, C. Chan, S. A. Campbell. Indecision is neural decision making models. Math. Model. Nat. Phenom. 5 (2010), 125–145. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  42. J. Milton, J. Lippai, R. Bellows, A. Blomberg, A. Kamimura, T. Ohira. Visuomotor tracking tasks with delayed pursuit and escape. 8th International Conference on Multibody Systems, Nonlinear Dynamics and Control (2011). Washington, D. C. (DETC2011-47312). [Google Scholar]
  43. P. J. Nahin PJ. Chases and escapes: The mathematics of pursuit and evasion. Princeton University Press, Princeton, New Jersey (2007). [Google Scholar]
  44. [Google Scholar]
  45. T. Ohira, J. Milton. Delayed random walks: Investigating the interplay between noise and delays. In: Delay Differential Equations: Recent Advances and New Directions, edited by B. Balachandran, T. Kalmár–Nagy and D. E. Gilman, Springer–Verlag, New York, pp. 305–335 (2009). [Google Scholar]
  46. F. Patzelt, M. Riegel, U. Ernst, K. Pawelzik. Self-organized critical noise amplification in human closed loop control. Front. Comp. Neurosci. 1 (2007), Article 4, 1–9. [Google Scholar]
  47. I. J. Pinter, R. von Swigchem, A. J. Knoek van Soet, L. A. Rozendaal. The dynamics of postural sway cannot be captured using a one-segment inverted pendulum model: A PCA on segment rotations during unperturbed stance. J. Neurophysiol. 100 (2008), 3197–3208. [CrossRef] [PubMed] [Google Scholar]
  48. A. B. Pippard. The inverted pendulum. Eur. J. Physics 8 (1987), 203–206. [CrossRef] [Google Scholar]
  49. [Google Scholar]
  50. [Google Scholar]
  51. [Google Scholar]
  52. [Google Scholar]
  53. S. H. Scott. Optimal feedback control and the neural basis of volitional motor control. Nature Rev, Neurosci. 5 (2004), 534–546. [Google Scholar]
  54. J. R. Stirling, M. S. Zakynthinaki. Stability and the maintenance of balance following a perturbation from quiet stance. Chaos 14 (2004), 96–105. [Google Scholar]
  55. G. Stepan. Delay effects in the human sensory system during balancing. Phil. Trans. Roy. Soc. A 367 (2009), 1195–1212. [CrossRef] [Google Scholar]
  56. N. Stepp. Anticipation in feedback–delayed manual tracking tracking of a chaotic oscillator. Exp. Brain Res. 198 (2009), 521–525. [CrossRef] [PubMed] [Google Scholar]
  57. A. Straw. An open–source library for realtime visual stimulus generation. Frontiers Neuroinformatics 11 (2008): doi: 10.3389.neuro.11.004:2008. [Google Scholar]
  58. A. D. Straw, M. H. Dickinson. Motmot, an open–source toolkit for realtime video acquisition and analysis. Source Code for Biology and Medicine (2010). doi: 10.1186/1751-0473-4-5. [Google Scholar]
  59. T. Vicsek. Closing in on evaders. Nature 466 (2010), 43–44. [Google Scholar]
  60. S. Vogel. Comparative Biomechanics: Life’s physical world. Princeton University Press, New Jersey (2003). [Google Scholar]
  61. H. U. Voss. Anticipating chaotic synchronization. Phys. Rev. E 61 (2000), 5115–5119. [Google Scholar]
  62. D. A. Winter, A. e. Patla, F. Prince, M. Ishac, K. Gielo–Perczak. Stiffness control in quiet standing. J. Neurophysiol. 80 (1998), 1211-1221. [PubMed] [Google Scholar]
  63. M. S. Zakynthinaki, J. M. Madera Milla, A. López de Durana, C. A. Cordent Martinez, G. Rodriguez Romo, M. Stillero Quintana, J. Samperd Molinuevo. Rotated balance in humans due to repetitive rotational movement. Chaos 20 (2010), 013118. [Google Scholar]
  64. V. Zatsiorsky. Biomechanics in Sports: Performance enhancement and injury prevention. Blackwell Science, Malden, MA (2000). [Google Scholar]

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