Neurobiological Models of Two-Choice Decision Making Can Be Reduced to a One-Dimensional Nonlinear Diffusion Equation
Figure 2
Diagram of the energy E(X) as a function of the difference in inputs Δν and the mean input to two populations in a winner-take-all network.
The populations are shown schematically as circles and the respective inputs as arrows. The relative level of input to the populations is represented by the spike trains “recorded” from the input arrows. (A) The energy E(X) as a function of the difference in inputs Δν shown for . Two cases are shown. Case 1, in green: both populations receive the same average input. This results in a symmetric energy function. Case 2, in black: population B receives more input than population A. This tilts the energy function, biasing the probability of choosing population B over A. (B) The energy E(X) as a function of the mean input
shown for Δν = 0 (both populations receive the same mean input). Three cases are shown. Case 1, in green:
. This results in a relatively flat energy function with zero curvature at zero. Case 2, in red:
. This results in a local minimum in the energy function. The system must escape over one of the two barriers for a decision to be made. Case 3, in blue:
. Here the inputs are large enough to transform the local minimum to a local maximum in the energy, making decisions faster and less accurate.