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PLOS ONE  2013 

Complexity Reduction of Rate-Equations Models for Two-Choice Decision-Making

DOI: 10.1371/journal.pone.0080820

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Abstract:

We are concerned with the complexity reduction of a stochastic system of differential equations governing the dynamics of a neuronal circuit describing a decision-making task. This reduction is based on the slow-fast behavior of the problem and holds on the whole phase space and not only locally around the spontaneous state. Macroscopic quantities, such as performance and reaction times, computed applying this reduction are in agreement with previous works in which the complexity reduction is locally performed at the spontaneous point by means of a Taylor expansion.

References

[1]  Ratcliff R, Smith P (2004) A comparison of sequential sampling sampling models for two-choice reaction time. Psychol Rev 111: 333–367.
[2]  Romo R, Salinas E (2001) Touch and go: Decision-making mechanisms in somatosensation. Annu Rev Neurosci 24: 107–137.
[3]  Romo R, Salinas E (2003) Flutter discrimination: neural codes, perception, memory and decision-making. Nature Reviews Neuroscience 4: 203–218.
[4]  Shadlen M, Newsome W (2001) Neural basis of a perceptual decision in the parietal cortex (area lip) of the rhesus monkey. J Neurophysiol 86: 1916–1936.
[5]  Roitman J, Shadlen M (2002) Response of neurons in the lateral intraparietal area during a com-bined visual discrimination reaction time task. J Neurosci 22: 9475–9489.
[6]  Huk A, Shadlen M (2005) Neural activity in macaque parietal cortex reects temporal integration of visual motion signals during perceptual decision making. J Neurosci 25: 10420–10436.
[7]  Wang X (2002) Probabilistic decision making by slow reverberation in cortical circuits. Neuron 36: 955–968.
[8]  Wong K, Wang X (2006) A recurrent network mechanism of time integration in perceptual decisions. J Neurosci 26: 1314–1328.
[9]  Lo C, Wang X (2006) Cortico-basal ganglia circuit mechanism for a decision threshold in reaction time tasks. Nat Neurosci 9: 956–963.
[10]  Roxin A, Ledberg A (2008) Neurobiological models of two-choice decision making can be reduced to a one-dimensional nonlinear diffusion equation. PLoS Computational Biology 4: 43–100.
[11]  Crawford J (1991) Introduction to bifurcation theory. Rev Mod Phys 63: 991–1037.
[12]  Berglund N, Gentz B (2005) Noise-induced phenomena in slow-fast dynamical systems. a sample-paths approach. Springer, Probability and its Applications.
[13]  Deco G, Martí D (2007) Deterministic analysis of stochastic bifurcations in multi-stable neurody-namical systems. Biol Cybern 96: 487–496.
[14]  Carrillo J, Cordier S, Mancini S (2013) One dimensional Fokker-Planck reduced dynamics of decision making models in computational neuroscience. Comm Math Sci 11: 523–540.
[15]  Hartman P (1960) A lemma in the theory of structural stability of differential equations. Proc Amer Math Soc 11: 610–620.
[16]  Gardiner C (1985) Handbook of stochastic methods for physics, chemistry and the natural sciences. Springer.
[17]  Carrillo J, Cordier S, Mancini S (2011) A decision-making Fokker-Planck model in computational neuroscience. J Math Biol 63: 801–830.
[18]  Holley R, Stroock D (1987) Logarithmic Sobolev inequalities and stochastic Ising models. J Statist Phys 46: 1159–1194.
[19]  Arnold A, Markowich P, Toscani G, Unterreiter A (2001) On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations. Comm Partial Differential Equations 26: 43–100.

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