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, interesting synchronization phenomena are observed. We investigate the formation of spatiotemporal patterns in both one-and two-dimensional oscillator lattices with periodic boundary conditions and comment on the role of dimensionality.

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Timms, L., and L.Q. English. Synchronization in Phase-Coupled Kuramoto Oscillator Networks with Axonal Delay and Synaptic Plasticity. Physical Review E 89, no. 3 (2014): e032906. https://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.032906