Neurobiological Models of Two-Choice Decision Making Can Be Reduced to a One-Dimensional Nonlinear Diffusion Equation
Figure 3
Fit to data from Roitman and Shadlen ([21], Table 2) with the nonlinear diffusion equation (Equation 8) and subsequent match with system of rate equations.
Black symbols: experimental data. Error bars represent approximate 95% confidence intervals. Lines: solution of Equation 8. Red symbols: simulated data from a system of rate equations (Equations 11–13). (A) Reaction times on correct and error trials as a function of coherence. Circles (solid line) and diamonds (dotted line) are for correct and error trials respectively. (B) Fraction of correct responses as a function of coherence. Experimental data are shown as crosses. Parameter values for Equation 8: ηΔν = coherence×6.6667e−6, , and σ = 0.00135. A fixed offset of 230 ms is added to the reaction times. We choose parameter values in the system of rate equations to yield precisely these parameters in Equation 8. See Materials and Methods for values.