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

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Abstract

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.

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Notes

  1. The particular expression (5) is used for simplicity. Numerical simulations of the model using other similar functions a(θ) revealed no substantial differences in the dynamics and statistical properties of control activation.

References

  • 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):e62,956

    Article  Google Scholar 

  • 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 149–168

    Chapter  Google Scholar 

  • 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 58:517–523

    Article  Google Scholar 

  • 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):588–615

    Article  PubMed  Google Scholar 

  • 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):473–495

    Article  PubMed  Google Scholar 

  • Cabrera J, Milton J (2002) On-off intermittency in a human balancing task. Phys Rev Lett 89(15):158,702

    Article  Google Scholar 

  • Cabrera J, Milton J (2012) Stick balancing, falls and Dragon-Kings. Eur Phys J Spec Top 205(1):231–241

    Article  Google Scholar 

  • Gawthrop P, Loram I, Lakie M, Gollee H (2011) Intermittent control: a computational theory of human control. Biol Cybern 104(1–2):31–51

    Article  PubMed  Google Scholar 

  • Haken H (1996) Principles of brain functioning. Springer, New York

    Book  Google Scholar 

  • Kapitza P (1951) Dynamic stability of a pendulum with an oscillating point of suspension. J Exp Theor Phys 21(5):588–597

    Google Scholar 

  • Kelso JS (1995) Dynamic patterns: The self-organization of brain and behavior. MIT press, Cambridge

    Google Scholar 

  • Kwakernaak H, Sivan R (1972) Linear optimal control systems. Wiley-Interscience, New York

    Google Scholar 

  • Lindner B, Schimansky-Geier L (2001) Transmission of noise coded versus additive signals through a neuronal ensemble. Phys Rev Lett 86(14):2934

    Article  CAS  PubMed  Google Scholar 

  • 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):1041–1053

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Loram I, Maganaris C, Lakie M (2005a) Human postural sway results from frequent, ballistic bias impulses by soleus and gastrocnemius. J Physiol 564(1):295–311

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • 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):281–293

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • 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):307–324

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Lubashevsky I, Wagner P, Mahnke R (2003) Rational-driver approximation in car-following theory. Phys Rev E 68(5):056,109

    Article  Google Scholar 

  • Mahnke R, Kaupuzs J, Lubashevsky I (2009) Physics of stochastic processes: how randomness acts in time. WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

    Google Scholar 

  • Mayer H, Krechetnikov R (2012) Walking with coffee: why does it spill? Phys Rev E 85(4):046117

    Article  CAS  Google Scholar 

  • Milton J, Cabrera J, Ohira T (2008) Unstable dynamical systems: delays, noise and control. EPL (Europhys Lett) 83(4):48,001

    Article  Google Scholar 

  • 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):026,110–026,110

    Article  Google Scholar 

  • 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):e7427

    Article  PubMed Central  PubMed  Google Scholar 

  • Milton J (2011) The delayed and noisy nervous system: implications for neural control. J Neural Eng 8(6):065,005

    Article  Google Scholar 

  • Milton J (2013) Intermittent motor control: the ‘drift-and-act’ hypothesis. In: Milton J (ed) Progress in motor control. Springer, New York, pp 169–193

    Chapter  Google Scholar 

  • Moreno-Bote R, Rinzel J, Rubin N (2007) Noise-induced alternations in an attractor network model of perceptual bistability. J Neurophysiol 98(3):1125–1139

    Article  PubMed Central  PubMed  Google Scholar 

  • Roessler A (2005) Explicit order 1.5 schemes for the strong approximation of Itô stochastic differential equations. Proc Appl Math Mech 5(1):817–818

    Article  Google Scholar 

  • Rolls ET, Deco G (2010) The noisy brain: stochastic dynamics as a principle of brain function. Oxford University Press, Oxford

    Book  Google Scholar 

  • 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):704–709

    Article  CAS  PubMed  Google Scholar 

  • Tuller B, Case P, Ding M, Kelso J (1994) The nonlinear dynamics of speech categorization. J Exp Psychol Hum Percept Perform 20(1):3

    Article  CAS  PubMed  Google Scholar 

  • van Rooij I, Bongers RM, Haselager W (2002) A non-representational approach to imagined action. Cogn Sci 26(3):345–375

    Article  Google Scholar 

  • van Rooij MM, Favela LH, Malone M, Richardson MJ (2013) Modeling the dynamics of risky choice. Ecol Psychol 25(3):293–303

    Article  Google Scholar 

  • 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):1218

    Article  PubMed Central  PubMed  Google Scholar 

  • Zgonnikov A, Lubashevsky I (2014) Extended phase space description of human-controlled systems dynamics. Prog Theor Exp Phys 2014(3):033J02

    Article  Google Scholar 

  • 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):20140636

    Article  PubMed Central  PubMed  Google Scholar 

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Acknowledgments

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

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Authors and Affiliations

  1. University of Aizu, Ikki-machi Tsuruga, Aizuwakamatsu city, Fukushima, 965-8580, Japan

    Arkady Zgonnikov & Ihor Lubashevsky

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  1. Arkady Zgonnikov
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  2. Ihor Lubashevsky
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Correspondence to Arkady Zgonnikov.

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This article is part of the Special Issue on ‘Complexity in brain and cognition’ and has been edited by Cees van Leeuwen.

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Zgonnikov, A., Lubashevsky, I. Double-well dynamics of noise-driven control activation in human intermittent control: the case of stick balancing. Cogn Process 16, 351–358 (2015). https://doi.org/10.1007/s10339-015-0653-5

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