2024/03/20 by Shriya V. Nagpal, Gokul G. Nair, Nagpal, Shriya V. +5 · 2 citations
Computer Science · #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2403.13998
openalex publication_date 2024/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Networks of coupled nonlinear oscillators have been used to model circadian rhythms, flashing fireflies, Josephson junction arrays, high-voltage electric grids, and many other kinds of self-organizing systems. Recently, several authors have sought to understand how coupled oscillators behave when they interact according to a random graph. Here we consider interaction networks generated by a graphon model known as a W-random network, and examine the dynamics of an infinite number of identical phase oscillators. We show that with sufficient regularity on W, the solution to the dynamical system over a W-random network of size n converges in the L∞ norm to the solution of the infinite graphon system, with high probability as n→∞. We leverage this convergence result to explore synchronization for two classes of identical phase oscillators on Erdős-Rényi random graphs. This result suggests a framework for studying synchronization properties in large but finite random networks.