Neurobiological Models of Two-Choice Decision Making Can Be Reduced to a One-Dimensional Nonlinear Diffusion Equation
Figure 4
Fit to data from Figure 7 in Palmer, Huk, and Shadlen [10] with Equation 8 and subsequent match with system of rate equations.
Filled circles: experimental data. Lines: solution of nonlinear diffusion equation, Equation 8. Open squares: system of rate equations. Error bars represents approximate 95% confidence intervals. Data are from three sets of experiments in which subjects are instructed to respond with 0.5 s (blue) 1 s (red) and 2 s (black). (A) Reaction times on correct trials as a function of coherence for subject 1. (B): Fraction of correct responses as a function of coherence for subject 1. Parameter values from Equation 8 for subject 1: ηΔν = coherence×1.25e−5, σ = 0.00135, , and 0.012 for 2 s, 1 s, and 0.5 s trials, respectively. (C) Reaction times on correct trials as a function of coherence for subject 2. (D) Fraction of correct responses as a function of coherence for subject 2. Parameter values from Equation 8 for subject 2: ηΔν = coherence×1.25e−5, σ = 0.00135,
, and 0.008 for 2 s, 1 s, and 0.5 s trials, respectively. A fixed offset of 260 ms and 220 ms was added to RT for subjects 1 and 2, respectively. We choose parameter values in the system of rate equations to yield precisely these parameters in Equation 8. See Materials and Methods for values.