2013/07/31 by Liam Timms, L. Q. English, Lars Q. English · 4 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · Neuroscience · Physics and Astronomy · #Artificial intelligence #Artificial neural network #Computer science #Control theory (sociology) #Coupling (piping) #Hebbian theory #Kuramoto model #Materials science #Mathematics #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #Phase (matter) #Phase synchronization #Physics #Quantum mechanics #Slime Mold and Myxomycetes Research #Statistical physics #Synchronization (alternating current) #Synchronization networks #Topology (electrical circuits) #nlin.AO #q-bio.NC
paper · pdf · doi:10.1103/physreve.89.032906
9 pages, 8 figures
arxiv created 2013/07/31 · openalex publication_date 2014/03/10 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.