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Indecision in Neural Decision Making Models

Published online by Cambridge University Press:  10 March 2010

J. Milton ,
P. Naik ,
C. Chan  and
S. A. Campbell
J. Milton*
Affiliation:
Joint Science Department, The Claremont Colleges, Claremont, CA 91711, USA
P. Naik
Affiliation:
Pomona College, The Claremont Colleges, Claremont, CA 91711, USA
C. Chan
Affiliation:
Harvey Mudd College, The Claremont Colleges, Claremont, CA 91711, USA
S. A. Campbell
Affiliation:
Department of Applied Mathematics, University of Waterloo, Canada
*
* Corresponding author. E-mail: [email protected]
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Abstract

Computational models for human decision making are typically based on the properties of bistable dynamical systems where each attractor represents a different decision. A limitation of these models is that they do not readily account for the fragilities of human decision making, such as “choking under pressure”, indecisiveness and the role of past experiences on current decision making. Here we examine the dynamics of a model of two interacting neural populations with mutual time–delayed inhibition. When the input to each population is sufficiently high, there is bistability and the dynamics is determined by the relationship of the initial function to the separatrix (the stable manifold of a saddle point) that separates the basins of attraction of two co–existing attractors. The consequences for decision making include long periods of indecisiveness in which trajectories are confined in the neighborhood of the separatrix and wrong decision making, particularly when the effects of past history and irrelevant information (“noise”) are included. Since the effects of delay, past history and noise on bistable dynamical systems are generic, we anticipate that similar phenomena will arise in the setting of other physical, chemical and neural time–delayed systems which exhibit bistability.

Keywords

neural networkdecisioninhibitorytime delaybistability
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 2: Mathematics and neuroscience , 2010 , pp. 125 - 145
Copyright
© EDP Sciences, 2010

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References

Baer, S.M., Erneux, T. Rinzel, J.. The slow passage through a Hopf bifurcation: Delay, memory effects and resonance . SIAM J. Appl. Math., 49 (1989), 55–71.CrossRefGoogle Scholar
Beilock, S. L., Carr, T. H.. On the fragility of skilled performance: What governs choking under pressure? J. Exper. Psych.: Gen., 130 (2001), 701–725. CrossRefGoogle ScholarPubMed
Beilock, S. L., Culp, C. A., Holt, L. E. Carr, T. H.. More on the fragility of performance: Choking under pressure in mathematical problem solving . J. Exp. Psych., 133 (2004), No. 4, 584–600.CrossRefGoogle ScholarPubMed
Bialek, W. De Weese, M.. Random switching and optimal processing in the perception of ambiguous signals . Phys. Rev. Lett., 74 (1995), 3077–3079.CrossRefGoogle ScholarPubMed
Bogacz, R., Brown, E., Moehlis, J., Holmes, P., Cohen, J. D.. The physics of optimal decision making: A formal analysis of models of performance in two–alternative forced–choice tasks . Psych. Rev. (2006), 700–765. CrossRefGoogle ScholarPubMed
Borsellino, A., DeMarco, A., Allazetta, A., Rinsei, S. Bartolini, B.. Reversal time distribution in the perception of visual ambiguous stimuli . Kybernetik, 10 (1972), 139–144.CrossRefGoogle ScholarPubMed
Briggman, K. L., Abarbanel, H. D. I. Kristan Jr, W. B.. Optical imaging of neuronal populations during decision–making . Science 307 (2005), 896–901.CrossRefGoogle ScholarPubMed
Brown, E., Gao, J., Holmes, P., Bogacz, R., Gilzenrat, M. Cohen, J. D.. Simple neural networks that optimize decisions . Int. J. Bifurc. Chaos, 15 (2005), No. 3, 803–826.CrossRefGoogle Scholar
Cabrera, J. L. Milton, J. G.. On–off intermittency in a human balancing task . Phys. Rev. Lett., 89 (2002), 158702 CrossRefGoogle Scholar
Choi, P. J., Cai, L., Fieda, K. Xie, X. S.. A stochastic single–molecule event triggers phenotype switching of a bacterial cell . Science, 322 (2008), No. 5900, 442–446.CrossRefGoogle ScholarPubMed
Coe, B., Tomihara, K., Matsuzawa, M. Hikosaka, O.. Visual and anticipatory bias in three cortical eye fields of the monkey during an adaptive decision–making task . J. Neurosci., 22 (2002), 5081–5090.CrossRefGoogle ScholarPubMed
Cole, K. J. Rotella, D. L.. Old age impairs the use of arbitrary visual cues for predicitive control of fingertip forces during grip . Exp. Brain Res. 143 (2002), 35–41.CrossRefGoogle Scholar
Deco, G., Pérez–Sanagustin, M., de Lafuente, V. Romo, R.. Perceptual detection as a dynamical bistability phenomenon: A neurocomputational correlate of sensation . Proc. Natl. Acad. Sci. USA, 104 (2007), 20073–20077.CrossRefGoogle ScholarPubMed
B. Ermentrout. Simulating, Analyzing, and Animating Dynamical Systems: A guide to XPPAUT for researchers and students. SIAM, Philadelphia, 2002.
Eurich, C. W. Milton, J. G.. Noise–induced transitions in human postural sway . Phys. Rev. E, 54 (1996), 6681–6684.CrossRefGoogle ScholarPubMed
M. Fairweather. Skill learning principles: implications for coaching practice. In: N. Cross, J. Lyle, eds, The Coaching Process: Principles and Practice for Sport. Butterworth Heinemann, New York, 1999, pp. 113–129.
P. M. Fitts, M. I. Posner. Human performance. Brooks/Cole, Belmont, CA, 1967.
Foss, J., Longtin, A., Mensour, B. Milton, J. G.. Multistability and delayed recurrent loops . Phys. Rev. Lett., 76 (1996), 708–711.CrossRefGoogle ScholarPubMed
Foss, J., Moss, F. Milton, J.. Noise, multistability, and delayed recurrent loops . Phys. Rev. E, 55 (1997), 4536–4543.CrossRefGoogle Scholar
Freeman, W. J. Schneider, W. S.. Changes in spatial patterns of rabbit olfactory EEG with conditioning to odors . Psychophysiology, 19 (1982), 44–56.CrossRefGoogle ScholarPubMed
P. W. Glimcher, C. F. Camerer, E. Fehr, R. A. Poldrack, eds. Neuroeconomics: Decision–making and the Brain. Academic Press, New York, 2009.
Gotman, J.. Measurement of small time differences between EEG channels: method and application to epileptic seizure propagation . Electroencephalogr. Clin. Neurophysiol., 79 (1983), 403–412.Google Scholar
Grotta–Ragazzo, C., Pakdaman, K. Malta, C. P.. Metastability for delayed differential equations . Phys. Rev. E., 60 (1999), 6230–6233.CrossRefGoogle ScholarPubMed
Hatfield, B. D., Haufler, A. J., Hung, T.–M. Spalding, T. W.. Electroencephalographic studies of skilled psychomotor performance . J. Clin. Neurophysiol., 21 (2004), 144-156.CrossRefGoogle ScholarPubMed
B. D. Hatfield, C. H. Hillman. The psychophysiology of sport: a mechanistic understanding of the psychology of superior performance. In: Handbook of Sport Psychology (R. N. Singer, H. A. Hausenblas, C. M. Janelle, eds). Wiley & Sons, New York, 2001, pp. 362–386.
Jeannerod, M. Decety, J.. Mental motor imagery: a window into the representational stages of action . Curr. Opin. Neurobiol., 5 (1995), 727–732.CrossRefGoogle Scholar
Kim, J. N. Shadlen, M. N. Neural correlates of a decision in the dorsolateral prefrontal cortex of the macaque . Nature Neuroscience, 2 (1999), 176–185.CrossRefGoogle ScholarPubMed
V. B. Kolmanovskii, V. R. Nosov, V. R. Stability of Functional Differential Equations. Academic Press, London, 1986.
P. Kruse, M. Stadler, eds. Ambiguity in Mind and Nature: Multistable cognitive phenomena. Springer, New York, 1995.
Levine, D. S. Prueitt, P. S.. Modeling some effects of frontal lobe damage – novelty and preservation . Neural Net. 2 (1989), 103–116.CrossRefGoogle Scholar
Losson, J., Mackey, M. C. Longtin, A. Solution multistability in first order nonlinear delay differential equations . Chaos 3 (1993), 167–176.CrossRefGoogle Scholar
Mazurek, M. E., Roitman, J. D., Ditterich, J. Shadlen, M. N.. A role for neural integrators in perceptual decision making . Cereb. Cortex, 13 (2003), 1257–1269.CrossRefGoogle ScholarPubMed
R. Miller. What is the contribution of axonal conduction delay to temporal structure in brain dynamics?. In: Oscillatory Event–related Brain Dynamics (C. Pantev, ed). Plenum Press: New York, 1994, pp. 53–57.
B. Milner. Some effects of frontal lobectomy in man. In: The frontal granular cortex and behavior (J. Warren, K. Akert, eds). McGraw–Hill: New York, 1964, pp. 313–334.
J. Milton, ed. Focus Issue on Bipedal Locomotion: From robots to humans. Chaos, 19 (2009).
Milton, J. G., Cabrera, J. L. Ohira, T.. Unstable dynamical systems: Delays, noise and control . EPL, 83 (2008), 48001 CrossRefGoogle Scholar
Milton, J. G., Small, S. S., Solodkin, A.. On the road to automatic: Dynamic aspects in the development of expertise . J. Clin. Neurophysiol., 21 (2004), no. 3, 134–143. CrossRefGoogle ScholarPubMed
Milton, J., Solodkin, A., Hlustik, P. Small, S. L.. The mind of expert motor performance is cool and focused . NeuroImage, 35 (2007), 804–813.CrossRefGoogle ScholarPubMed
Milton, J., Small, S. L. Solodkin, A.. Imaging motor imagery: Methodological issues related to expertise . Methods, 45 (2008), 336–341.CrossRefGoogle ScholarPubMed
Oishi, K. Maeshima, T.. Autonomic nervous system activities during motor imagery in elite athletes . J. Clin. Neurophysiol., 21 (2004), 170–179.CrossRefGoogle ScholarPubMed
Pakdaman, K., Grotta–Ragazzo, C. Malta, C. P.. Transient regime duration in continuous–time neural networks with delay . Phys. Rev. E, 58 (1998), 3623–3627.CrossRefGoogle Scholar
Pakdaman, K., Grotta–Ragazzo, C., Malta, C. P., Arino, O. Vibert, J.–F.. Effect of delay on the boundary of the basin of attraction in a system of two neurons . Neural Networks, 11 (1998), 509–519.CrossRefGoogle Scholar
Riani, M. Simonotto, E.. Stochastic resonance in the perceptual interpretation of ambiguous figures: A neural network approach . Phys. Rev. Lett., 72 (1994), 3120–3123.CrossRefGoogle Scholar
Rinzel, J. Baer, S. M.. Threshold for repetitive activity for a slow stimulus ramp: A memory effect and its dependence on fluctuations . Biophys. J., 54 (1988), 551–555.CrossRefGoogle ScholarPubMed
Sanfey, A.G., Rilling, J. K., Aronson, J. A., Nystrom, L. E. Cohen, J. D.. The neural basis of economic decision–making in the ultimatum game . Science, 300 (2003), 1755–1758.CrossRefGoogle ScholarPubMed
Schall, J. D.. Neural basis of deciding, choosing, and acting . Nat. Neurosci. 2 (2001), 33–42.CrossRefGoogle ScholarPubMed
Seymour, B., Daw, N., Dayan, P., Somger, T. Dolan, R.. Differential encoding of losses and gains in the human straitum . J. Neurosci., 27 (2007), 4826–4831.CrossRefGoogle Scholar
Shadlen, M. N. Newsome, W. T.. Neural basis of a perceptual decision in the parietal cortex (area LIP) of the rhesus monkey . J. Neurophysiol., 86 (2001), 1916–1936.CrossRefGoogle ScholarPubMed
G. Stépán. Retarded Dynamical Systems: Stability and Characteristic Functions. Longman Group, Essex, 1989.
Stépán, G. Insperger, T.. Stability of time–periodic and delayed systems - a route to act–and–wait control . Annu. Rev. Control, 30 (2006), 159–168.CrossRefGoogle Scholar
Takác, P.. Domains of attraction of generic omega–limit sets for strongly monotone semi–flows . Zeitschrift fur Analysis und ihre Answendungen, 10 (1991), 275–317.CrossRefGoogle Scholar
Thielscher, A. Pessoa, L.. Neural correlates of perceptual choice and decision making during fear–disgust discrimination . J. Neurosci., 27 (2007), 2908–2917.CrossRefGoogle ScholarPubMed
Usher, M. L.McClelland, J.. The time course of perceptual choice: The leaky, competing accumulator model . Psychol. Rev., 108 (2001), 550–592.CrossRefGoogle ScholarPubMed
Wang, X.–J.. Probabilistic decisions making by slow reverberation in cortical circuits . Neuron, 36 (2002), 955–968.CrossRefGoogle Scholar
Westen, D., Blagov, P. S., Harenski, K., Kilts, C. Hamann, S.. Neural bases of motivated reasoning: An fMRI study of emotional constraints on partisan political judgement in the 2004 U. S. presidential election . J. Cog. Neuroscience, 18 (2006), No. 11, 1947–1958.CrossRefGoogle ScholarPubMed
Wong, K.–F. Wang, X.–J.. A recurrent network mechanism of time integration in perceptual decisions . J. Neurosci., 26 (2006), 1314–1328.CrossRefGoogle ScholarPubMed