Indecision in neural decision making models

Mathematical Modelling of Natural Phenomena

Volumn 5, Issue 2, 2010, Pages 125-145

  Milton, J ^a   Naik, P ^b   Chan, C ^c   Campbell, S A ^d  

^a The Claremont Colleges   (United States)

^b POMONA COLLEGE   (United States)

^c HARVEY MUDD COLLEGE   (United States)

^d UNIVERSITY OF WATERLOO   (Canada)

Author keywords

bistability; decision; inhibitory; neural network; time delay

Indexed keywords

BASINS OF ATTRACTION; BISTABLES; CO-EXISTING ATTRACTORS; COMPUTATIONAL MODEL; DECISION; DECISION MAKING MODELS; HUMAN DECISION MAKING; INHIBITORY; INITIAL FUNCTIONS; NEURAL POPULATIONS; ON CURRENTS; SADDLE POINT; SEPARATRIX; STABLE MANIFOLD; TIME-DELAYED SYSTEMS;

DYNAMICAL SYSTEMS; NEURAL NETWORKS;

DECISION MAKING;

EID: 77953915764     PISSN: 09735348     EISSN: 17606101     Source Type: Journal    
DOI: 10.1051/mmnp/20105205     Document Type: Review

References (56)

1. S. M. Baer, T. Erneux, J. Rinzel. The slow passage through a Hopf bifurcation: Delay, memory effects and resonance. SIAM J. Appl. Math., 49 (1989), 55-71.
2. S. L. Beilock, T. H. Carr. On the fragility of skilled performance: What governs choking under pressure? J. Exper. Psych.: Gen., 130 (2001), 701-725. (Pubitemid 33594791)
3. S. L. Beilock, C. A. Culp, L. E. Holt, T. H. Carr. More on the fragility of performance: Choking under pressure in mathematical problem solving. J. Exp. Psych., 133 (2004), No. 4, 584-600. (Pubitemid 39666187)
4. W. Bialek, M. De Weese. Random switching and optimal processing in the perception of ambiguous signals. Phys. Rev. Lett., 74 (1995), 3077-3079.
5. R. Bogacz, E. Brown, J. Moehlis, P. Holmes, J. D. Cohen. The physics of optimal decision making: A formal analysis of models of performance in two-alternative forced- choice tasks. Psych. Rev. (2006), 700-765. (Pubitemid 44629916)
6. A. Borsellino, A. DeMarco, A. Allazetta, S. Rinsei, B. Bartolini. Reversal time distri- bution in the perception of visual ambiguous stimuli. Kybernetik, 10 (1972), 139-144.
7. K. L. Briggman, H. D. I. Abarbanel, W. B. Kristan Jr. Optical imaging of neuronal populations during decision-making. Science 307 (2005), 896-901. (Pubitemid 40229220)
8. E. Brown, J. Gao, P. Holmes, R. Bogacz, M. Gilzenrat, J. D. Cohen. Simple neural networks that optimize decisions. Int. J. Bifurc. Chaos, 15 (2005), No. 3, 803-826. (Pubitemid 40878385)
9. J. L. Cabrera, J. G. Milton. On-off intermittency in a human balancing task. Phys. Rev. Lett., 89 (2002), 158702.
10. P. J. Choi, L. Cai, K. Fieda, X. S. Xie. A stochastic single-molecule event triggers phenotype switching of a bacterial cell. Science, 322 (2008), No. 5900, 442-446.
11. B. Coe, K. Tomihara, M. Matsuzawa, O. Hikosaka. Visual and anticipatory bias in three cortical eye fields of the monkey during an adaptive decision-making task. J. Neurosci., 22 (2002), 5081-5090. (Pubitemid 37465621)
12. K. J. Cole, D. L. Rotella. Old age impairs the use of arbitrary visual cues for predicitive control of fingertip forces during grip. Exp. Brain Res. 143 (2002), 35-41. (Pubitemid 34507541)
13. G. Deco, M. Pérez-Sanagustin, V. de Lafuente, R. Romo. Perceptual detection as a dynamical bistability phenomenon: A neurocomputational correlate of sensation. Proc. Natl. Acad. Sci. USA, 104 (2007), 20073-20077.
14. B. Ermentrout. Simulating, Analyzing, and Animating Dynamical Systems: A guide to XPPAUT for researchers and students. SIAM, Philadelphia, 2002.
15. C. W. Eurich, J. G. Milton. Noise-induced transitions in human postural sway. Phys. Rev. E, 54 (1996), 6681-6684. (Pubitemid 126587082)
16. M. Fairweather. Skill learning principles: implications for coaching practice. In: N. Cross, J. Lyle, eds, The Coaching Process: Principles and Practice for Sport. But- terworth Heinemann, New York, 1999, pp. 113-129.
17. P. M. Fitts, M. I. Posner. Human performance. Brooks/Cole, Belmont, CA, 1967.
18. J. Foss, A. Longtin, B. Mensour, J. G. Milton. Multistability and delayed recurrent loops. Phys. Rev. Lett., 76 (1996), 708-711. (Pubitemid 126639502)
19. J. Foss, F. Moss, J. Milton. Noise, multistability, and delayed recurrent loops. Phys. Rev. E, 55 (1997), 4536-4543. (Pubitemid 127612806)
20. W. J. Freeman, W. S. Schneider. Changes in spatial patterns of rabbit olfactory EEG with conditioning to odors. Psychophysiology, 19 (1982), 44-56. (Pubitemid 12172277)
21. P. W. Glimcher, C. F. Camerer, E. Fehr, R. A. Poldrack, eds. Neuroeconomics: Decision-making and the Brain. Academic Press, New York, 2009.
22. J. Gotman. Measurement of small time differences between EEG channels: method and application to epileptic seizure propagation. Electroencephalogr. Clin. Neurophysiol., 79 (1983), 403-412.
23. C. Grotta-Ragazzo, K. Pakdaman, C. P. Malta. Metastability for delayed differential equations. Phys. Rev. E., 60 (1999), 6230-6233. (Pubitemid 129651901)
24. B. D. Hatfield, A. J. Haufler, T.-M. Hung, T. W. Spalding. Electroencephalographic studies of skilled psychomotor performance. J. Clin. Neurophysiol., 21 (2004), 144-156. (Pubitemid 40238533)
25. B. D. Hatfield, C. H. Hillman. The psychophysiology of sport: a mechanistic under- standing 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.
26. M. Jeannerod, J. Decety. Mental motor imagery: a window into the representational stages of action. Curr. Opin. Neurobiol., 5 (1995), 727-732. (Pubitemid 26042621)
27. J. N. Kim, M. N. Shadlen, Neural correlates of a decision in the dorsolateral prefrontal cortex of the macaque. Nature Neuroscience, 2 (1999), 176-185. (Pubitemid 30491319)
28. V. B. Kolmanovskii, V. R. Nosov, V. R. Stability of Functional Differential Equations. Academic Press, London, 1986.
29. P. Kruse, M. Stadler, eds. Ambiguity in Mind and Nature: Multistable cognitive phe- nomena. Springer, New York, 1995.
30. D. S. Levine, P. S. Prueitt. Modeling some effects of frontal lobe damage - novelty and preservation. Neural Net. 2 (1989), 103-116.
31. J. Losson, M. C. Mackey, and A. Longtin, Solution multistability in first order nonlinear delay differential equations. Chaos 3 (1993), 167-176.
32. M. E. Mazurek, J. D. Roitman, J. Ditterich, M. N. Shadlen. A role for neural integrators in perceptual decision making. Cereb. Cortex, 13 (2003), 1257-1269. (Pubitemid 37323002)
33. 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.
34. 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.
35. J. Milton, ed. Focus Issue on Bipedal Locomotion: From robots to humans. Chaos, 19 (2009).
36. J. G. Milton, J. L. Cabrera, T. Ohira. Unstable dynamical systems: Delays, noise and control. EPL, 83 (2008), 48001.
37. 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), no. 3, 134-143. (Pubitemid 40238532)
38. J. Milton, A. Solodkin, P. Hlustik, S. L. Small. The mind of expert motor performance is cool and focused. NeuroImage, 35 (2007), 804-813. (Pubitemid 46400566)
39. J. Milton, S. L. Small, A. Solodkin. Imaging motor imagery: Methodological issues related to expertise. Methods, 45 (2008), 336-341.
40. K. Oishi, T. Maeshima. Autonomic nervous system activities during motor imagery in elite athletes. J. Clin. Neurophysiol., 21 (2004), 170-179. (Pubitemid 40238535)
41. K. Pakdaman, C. Grotta-Ragazzo, C. P. Malta. Transient regime duration in continuous-time neural networks with delay. Phys. Rev. E, 58 (1998), 3623-3627. (Pubitemid 128603399)
42. K. Pakdaman, C. Grotta-Ragazzo, C. P. Malta, O. Arino, J. -F. Vibert. Effect of delay on the boundary of the basin of attraction in a system of two neurons. Neural Networks, 11 (1998), 509-519. (Pubitemid 28351086)
43. M. Riani, E. Simonotto. Stochastic resonance in the perceptual interpretation of am- biguous figures: A neural network approach. Phys. Rev. Lett., 72 (1994), 3120-3123. (Pubitemid 24975336)
44. J. Rinzel, S. M. Baer. Threshold for repetitive activity for a slow stimulus ramp: A memory effect and its dependence on fluctuations. Biophys. J., 54 (1988), 551-555.
45. A. G. Sanfey, J. K. Rilling, J. A. Aronson, L. E. Nystrom, J. D.Cohen. The neural basis of economic decision-making in the ultimatum game. Science, 300 (2003), 1755-1758. (Pubitemid 36712573)
46. J. D. Schall. Neural basis of deciding, choosing, and acting. Nat. Neurosci. 2 (2001), 33-42. (Pubitemid 33673347)
47. B. Seymour, N. Daw, P. Dayan, T. Somger, R. Dolan. Differential encoding of losses and gains in the human straitum. J. Neurosci., 27 (2007), 4826-4831. (Pubitemid 46699059)
48. M. N. Shadlen, W. T. Newsome. Neural basis of a perceptual decision in the parietal cortex (area LIP) of the rhesus monkey. J. Neurophysiol., 86 (2001), 1916-1936. (Pubitemid 32953239)
49. G. Stépán. Retarded Dynamical Systems: Stability and Characteristic Functions. Long- man Group, Essex, 1989.
50. G. Stépán, T. Insperger. Stability of time-periodic and delayed systems - a route to act-and-wait control. Annu. Rev. Control, 30 (2006), 159-168. (Pubitemid 44780176)
51. P. Takác. Domains of attraction of generic omega-limit sets for strongly monotone semi-flows. Zeitschrift fur Analysis und ihre Answendungen, 10 (1991), 275-317.
52. A. Thielscher, L. Pessoa. Neural correlates of perceptual choice and decision making during fear-disgust discrimination. J. Neurosci., 27 (2007), 2908-2917. (Pubitemid 46438981)
53. M. Usher, J. L.McClelland. The time course of perceptual choice: The leaky, competing accumulator model. Psychol. Rev., 108 (2001), 550-592. (Pubitemid 33604137)
54. X.-J. Wang. Probabilistic decisions making by slow reverberation in cortical circuits. Neuron, 36 (2002), 955-968. (Pubitemid 35447866)
55. D. Westen, P. S. Blagov, K. Harenski, C. Kilts, S. Hamann. 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. (Pubitemid 44674292)
56. K.-F. Wong, X.-J. Wang. A recurrent network mechanism of time integration in per- ceptual decisions. J. Neurosci., 26 (2006), 1314-1328. (Pubitemid 43237063)