Mathematical Modelling of Natural Phenomena

Research Article

Indecision in Neural Decision Making Models

J. Miltona1 c1, P. Naika2, C. Chana3 and S. A. Campbella4

a1 Joint Science Department, The Claremont Colleges, Claremont, CA 91711, USA

a2 Pomona College, The Claremont Colleges, Claremont, CA 91711, USA

a3 Harvey Mudd College, The Claremont Colleges, Claremont, CA 91711, USA

a4 Department of Applied Mathematics, University of Waterloo, Canada


Computational models for human decision making are typically based on the properties of bistable dynamical systems where each attractor represents a different decision. A limitation of these models is that they do not readily account for the fragilities of human decision making, such as “choking under pressure”, indecisiveness and the role of past experiences on current decision making. Here we examine the dynamics of a model of two interacting neural populations with mutual time–delayed inhibition. When the input to each population is sufficiently high, there is bistability and the dynamics is determined by the relationship of the initial function to the separatrix (the stable manifold of a saddle point) that separates the basins of attraction of two co–existing attractors. The consequences for decision making include long periods of indecisiveness in which trajectories are confined in the neighborhood of the separatrix and wrong decision making, particularly when the effects of past history and irrelevant information (“noise”) are included. Since the effects of delay, past history and noise on bistable dynamical systems are generic, we anticipate that similar phenomena will arise in the setting of other physical, chemical and neural time–delayed systems which exhibit bistability.

(Online publication March 10 2010)

Key Words:

  • neural network;
  • decision;
  • inhibitory;
  • time delay;
  • bistability

Mathematics Subject Classification:

  • 92C20;
  • 34K20;
  • 34K50


c1 Corresponding author. E-mail: