Towards a mathematical model of within-session operant responding.

Operant response rate changes within the course of a typical free-operant experimental session. These changes are orderly, and reliably demonstrated with subjects from different species, responding under different experimental conditions. Killeen (1995) postulated that the response rate changes are a function of the interplay between arousal and satiation and offered a mathematical model for this hypothesis. Here we analyze Killeen's model, demonstrating that, although solid in its principles, it presents some flaws in its implementation. Then, based on the same principles, we build and test a new model of within-session motivation dynamics. We also demonstrate that, by representing arousal as a variable that ranges between 0 and 1, we can obtain a surprisingly simple model of free-operant response rate.