Synchronization in Phase-Coupled Kuramoto Oscillator Networks with Axonal Delay and Synaptic Plasticity

TL;DR

This paper investigates how time-delay and synaptic plasticity influence synchronization in Kuramoto oscillator networks, revealing novel phenomena and pattern formations through analytical and numerical methods.

Contribution

It introduces a combined model of phase-coupled oscillators with delay and plasticity, exploring their effects on synchronization and pattern formation.

Findings

Novel synchronization phenomena observed with delay and plasticity

Formation of spatio-temporal patterns in oscillator lattices

Dimensionality impacts pattern dynamics

Abstract

We explore both analytically and numerically an ensemble of coupled phase-oscillators governed by a Kuramoto-type system of differential equations. However, we have included the effects of time-delay (due to finite signal-propagation speeds) and network plasticity (via dynamic coupling constants) inspired by the Hebbian learning rule in neuroscience. When time-delay and learning effects combine, novel synchronization phenomena are observed. We investigate the formation of spatio-temporal patterns in both one- and two-dimensional oscillator lattices with periodic boundary conditions and comment on the role of dimensionality.