Harmonic Memory in Phasor Neural Networks

Huygens unknowingly created a harmonic network when he mounted two pendulum clocks on a common support. The clocks were observed to synchronize—an early example of a harmonic network formed unintentionally when a designed system interacts with its substrate. Comparable substrate-mediated phenomena have been reported in biological systems. Motivated by Vinogradova’s comparator hypothesis in the limbic system, we show how a system based on canonical pendulum dynamics can realize a comparator-like mechanism in which latent harmonic structure is embedded in an interaction potential and revealed through frequency-controlled phase locking in the network of oscillators. In this framework, memories are not stored as static attractors but as oscillatory structures that are transiently expressed through resonance and phase locking. As control frequencies pass through locking regions, brief episodes of coherent high-frequency activity emerge across the system. The system developed here demonstrates how distributed oscillators can unify along a shared harmonic direction with fixed relative timing, producing system-level coherence without requiring explicit pairwise synchronization.