A piecewise linear, stochastic map model for the sequential trial strategy of discrete timing tasks

In this paper we present a piecewise linear, stochastic map model for discrete timing tasks that describes the trial to trial strategies in relation to a threshold for adaptive change beyond which the dynamics is purely stochastic. The model is a basic difference equation with three parameters, slope, threshold, and noise amplitude that are considered stationary in this fast dynamics performance model. The model fits experimental discrete timing data under conditions of knowledge of results and reveals the trial to trial strategies of creeping and bracketing in reducing error in relation to the target. Parameters derived from the data were also used for simulations from the model and good qualitative and quantitative fits were obtained. We close with a discussion of a four-dimensional generalization of our basic model that incorporates learning at multiple time-scales.