Star Networks Store 2^N Memories via Plasticity

This episode explores how a star-shaped network of phase oscillators, whose synaptic weights evolve through a plasticity rule based on phase differences, can settle into exactly 2^N distinct stable configurations, where N is the number of leaf nodes. Each leaf independently either synchronizes with the central hub — forming a strong one-directional synapse — or drifts freely in a near-disconnected state, encoding a binary pattern across the network. The result holds regardless of the hub's natural frequency relative to the leaves, and was analytically derived and numerically confirmed for networks up to nine leaves with 512 distinct stable states. Reference: Ratas, Pyragas & Tass (2021) "Multistability in a star network of Kuramoto-type oscillators with synaptic plasticity" Scientific Reports. https://doi.org/10.1038/s41598-021-89198-0