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arXiv · 2403.13998

Synchronization in random networks of identical phase oscillators: A graphon approach

Shriya V. Nagpal·Gokul G. Nair·Steven H. Strogatz·Francesca Parise
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Abstract

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 $L^{\infty}$ norm to the solution of the infinite graphon system, with high probability as $n\rightarrow\infty$. We leverage this convergence result to explore synchronization for two classes of identical phase oscillators on Erd\H{o}s-R\'enyi random graphs. This result suggests a framework for studying synchronization properties in large but finite random networks.

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Shriya V. Nagpal, Gokul G. Nair, Steven H. Strogatz, Francesca Parise. 2024-03-20. Synchronization in random networks of identical phase oscillators: A graphon approach. https://arxiv.org/abs/2403.13998

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