Meter Through Synchrony: Processing Rhythmical Patterns with Relaxation Oscillators

This dissertation uses a network of relaxation oscillators to beat along with temporal signals. Relaxation oscillators exhibit interspersed slow-fast movement and model a wide array of biological oscillations. The model is built up gradually: first a single relaxation oscillator is exposed to rhythms and shown to be good at finding downbeats in them. Then large networks of oscillators are mutually coupled in an exploration of their internal synchronization behavior. It is demonstrated that appropriate weights on coupling connections cause a network to form multiple pools of oscillators having stable phase relationships. This is a promising first step towards networks that can recreate a rhythmical pattern from memory. In the full model, a coupled network of relaxation oscillators is exposed to rhythmical patterns. It is shown that the network finds downbeats in patterns while continuing to exhibit good internal stability. A novel non-dynamical model of downbeat induction called the Normalized Positive (NP) clock model is proposed, analyzed, and used to generate comparison predictions for the oscillator model. The oscillator model compares favorably to other dynamical approaches to beat induction such as adaptive oscillators. However, the relaxation oscillator model takes advantage of intrinsic synchronization stability to allow the creation of large coupled networks. This research lays the groundwork for a long-term research goal, a robotic arm that responds to rhythmical signals by tapping along. It also opens the door to future work in connectionist learning of long rhythmical patterns.