Phase-oscillator computations as neural models of stimulus–response conditioning and response selection

The activity of collections of synchronizing neurons can be represented by weakly coupled nonlinear phase oscillators satisfying Kuramoto’s equations. In this article, we build such neural-oscillator models, partly based on neurophysiological evidence, to represent approximately the learning behavior predicted and confirmed in three experiments by well-known stochastic learning models of behavioral stimulus–response theory. We use three Kuramoto oscillators to model a continuum of responses, and we provide detailed numerical simulations and analysis of the three-oscillator Kuramoto problem, including an analysis of the stability points for different coupling conditions. We show that the oscillator simulation data are well-matched to the behavioral data of the three experiments.

► We propose neural oscillators to provide a brain model of behavioral stimulus–response theory.
► Our neural models make use of three weakly coupled oscillators satisfying Kuramoto’s equations.
► We show an analysis of the behavior of the solutions for the three-oscillator Kuramoto equations.
► We give detailed oscillator computations for stimulus–response conditioning and response selection.
► We use our simulations to compare oscillator-simulated data with empirical data from three behavioral experiments.