Cognitive Processing

, Volume 16, Issue 4, pp 351–358 | Cite as

Double-well dynamics of noise-driven control activation in human intermittent control: the case of stick balancing

  • Arkady ZgonnikovEmail author
  • Ihor Lubashevsky
Research Report


When facing a task of balancing a dynamic system near an unstable equilibrium, humans often adopt intermittent control strategy: Instead of continuously controlling the system, they repeatedly switch the control on and off. Paradigmatic example of such a task is stick balancing. Despite the simplicity of the task itself, the complexity of human intermittent control dynamics in stick balancing still puzzles researchers in motor control. Here we attempt to model one of the key mechanisms of human intermittent control, control activation, using as an example the task of overdamped stick balancing. In doing so, we focus on the concept of noise-driven activation, a more general alternative to the conventional threshold-driven activation. We describe control activation as a random walk in an energy potential, which changes in response to the state of the controlled system. By way of numerical simulations, we show that the developed model captures the core properties of human control activation observed previously in the experiments on overdamped stick balancing. Our results demonstrate that the double-well potential model provides tractable mathematical description of human control activation at least in the considered task and suggest that the adopted approach can potentially aid in understanding human intermittent control in more complex processes.


Intermittent motor control Stick balancing Stochastic modeling Bistable dynamics 



The work was supported in part by the JSPS “Grants-in-Aid for Scientific Research” Program, Grant 24540410-0001.


  1. Asai Y, Tateyama S, Nomura T (2013) Learning an intermittent control strategy for postural balancing using an EMG-based human-computer interface. PLoS One 8(5):e62,956CrossRefGoogle Scholar
  2. Balasubramaniam R (2013) On the control of unstable objects: the dynamics of human stick balancing. In: Balasubramaniam R (ed) Progress in motor control. Springer, New York, pp 149–168CrossRefGoogle Scholar
  3. Bormann R, Cabrera JL, Milton JG, Eurich CW (2004) Visuomotor tracking on a computer screen—an experimental paradigm to study the dynamics of motor control. Neurocomputing 58:517–523CrossRefGoogle Scholar
  4. Bottaro A, Casadio M, Morasso PG, Sanguineti V (2005) Body sway during quiet standing: is it the residual chattering of an intermittent stabilization process? Hum Mov Sci 24(4):588–615CrossRefPubMedGoogle Scholar
  5. Bottaro A, Yasutake Y, Nomura T, Casadio M, Morasso P (2008) Bounded stability of the quiet standing posture: an intermittent control model. Hum Mov Sci 27(3):473–495CrossRefPubMedGoogle Scholar
  6. Cabrera J, Milton J (2002) On-off intermittency in a human balancing task. Phys Rev Lett 89(15):158,702CrossRefGoogle Scholar
  7. Cabrera J, Milton J (2012) Stick balancing, falls and Dragon-Kings. Eur Phys J Spec Top 205(1):231–241CrossRefGoogle Scholar
  8. Gawthrop P, Loram I, Lakie M, Gollee H (2011) Intermittent control: a computational theory of human control. Biol Cybern 104(1–2):31–51CrossRefPubMedGoogle Scholar
  9. Haken H (1996) Principles of brain functioning. Springer, New YorkCrossRefGoogle Scholar
  10. Kapitza P (1951) Dynamic stability of a pendulum with an oscillating point of suspension. J Exp Theor Phys 21(5):588–597Google Scholar
  11. Kelso JS (1995) Dynamic patterns: The self-organization of brain and behavior. MIT press, CambridgeGoogle Scholar
  12. Kwakernaak H, Sivan R (1972) Linear optimal control systems. Wiley-Interscience, New YorkGoogle Scholar
  13. Lindner B, Schimansky-Geier L (2001) Transmission of noise coded versus additive signals through a neuronal ensemble. Phys Rev Lett 86(14):2934CrossRefPubMedGoogle Scholar
  14. Loram ID, Lakie M (2002) Direct measurement of human ankle stiffness during quiet standing: the intrinsic mechanical stiffness is insufficient for stability. J Physiol 545(3):1041–1053PubMedCentralCrossRefPubMedGoogle Scholar
  15. Loram I, Maganaris C, Lakie M (2005a) Human postural sway results from frequent, ballistic bias impulses by soleus and gastrocnemius. J Physiol 564(1):295–311PubMedCentralCrossRefPubMedGoogle Scholar
  16. Loram ID, Maganaris CN, Lakie M (2005b) Active, non-spring-like muscle movements in human postural sway: how might paradoxical changes in muscle length be produced? J Physiol 564(1):281–293PubMedCentralCrossRefPubMedGoogle Scholar
  17. Loram I, Gollee H, Lakie M, Gawthrop P (2011) Human control of an inverted pendulum: is continuous control necessary? Is intermittent control effective? Is intermittent control physiological? J Physiol 589(2):307–324PubMedCentralCrossRefPubMedGoogle Scholar
  18. Lubashevsky I, Wagner P, Mahnke R (2003) Rational-driver approximation in car-following theory. Phys Rev E 68(5):056,109CrossRefGoogle Scholar
  19. Mahnke R, Kaupuzs J, Lubashevsky I (2009) Physics of stochastic processes: how randomness acts in time. WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimGoogle Scholar
  20. Mayer H, Krechetnikov R (2012) Walking with coffee: why does it spill? Phys Rev E 85(4):046117CrossRefGoogle Scholar
  21. Milton J, Cabrera J, Ohira T (2008) Unstable dynamical systems: delays, noise and control. EPL (Europhys Lett) 83(4):48,001CrossRefGoogle Scholar
  22. Milton J, Cabrera J, Ohira T, Tajima S, Tonosaki Y, Eurich C, Campbell S (2009a) The time-delayed inverted pendulum: implications for human balance control. Chaos 19(2):026,110–026,110CrossRefGoogle Scholar
  23. Milton J, Ohira T, Cabrera J, Fraiser R, Gyorffy J, Ruiz F, Strauss M, Balch E, Marin P, Alexander J (2009b) Balancing with vibration: a prelude for “drift and act” balance control. PLoS One 4(10):e7427PubMedCentralCrossRefPubMedGoogle Scholar
  24. Milton J (2011) The delayed and noisy nervous system: implications for neural control. J Neural Eng 8(6):065,005CrossRefGoogle Scholar
  25. Milton J (2013) Intermittent motor control: the ‘drift-and-act’ hypothesis. In: Milton J (ed) Progress in motor control. Springer, New York, pp 169–193CrossRefGoogle Scholar
  26. Moreno-Bote R, Rinzel J, Rubin N (2007) Noise-induced alternations in an attractor network model of perceptual bistability. J Neurophysiol 98(3):1125–1139PubMedCentralCrossRefPubMedGoogle Scholar
  27. Roessler A (2005) Explicit order 1.5 schemes for the strong approximation of Itô stochastic differential equations. Proc Appl Math Mech 5(1):817–818CrossRefGoogle Scholar
  28. Rolls ET, Deco G (2010) The noisy brain: stochastic dynamics as a principle of brain function. Oxford University Press, OxfordCrossRefGoogle Scholar
  29. Silberberg G, Bethge M, Markram H, Pawelzik K, Tsodyks M (2004) Dynamics of population rate codes in ensembles of neocortical neurons. J Neurophysiol 91(2):704–709CrossRefPubMedGoogle Scholar
  30. Tuller B, Case P, Ding M, Kelso J (1994) The nonlinear dynamics of speech categorization. J Exp Psychol Hum Percept Perform 20(1):3CrossRefPubMedGoogle Scholar
  31. van Rooij I, Bongers RM, Haselager W (2002) A non-representational approach to imagined action. Cogn Sci 26(3):345–375CrossRefGoogle Scholar
  32. van Rooij MM, Favela LH, Malone M, Richardson MJ (2013) Modeling the dynamics of risky choice. Ecol Psychol 25(3):293–303CrossRefGoogle Scholar
  33. Wagemans J, Feldman J, Gepshtein S, Kimchi R, Pomerantz JR, van der Helm PA, van Leeuwen C (2012) A century of Gestalt psychology in visual perception: II. Conceptual and theoretical foundations. Psychol Bull 138(6):1218PubMedCentralCrossRefPubMedGoogle Scholar
  34. Zgonnikov A, Lubashevsky I (2014) Extended phase space description of human-controlled systems dynamics. Prog Theor Exp Phys 2014(3):033J02CrossRefGoogle Scholar
  35. Zgonnikov A, Lubashevsky I, Kanemoto S, Miyazawa T, Suzuki T (2014) To react or not to react? Intrinsic stochasticity of human control in virtual stick balancing. J R Soc Interface 11(99):20140636PubMedCentralCrossRefPubMedGoogle Scholar

Copyright information

© Marta Olivetti Belardinelli and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.University of AizuAizuwakamatsu cityJapan

Personalised recommendations