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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.13998 |
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| _version_ | 1866914072780341248 |
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| author | Nagpal, Shriya V. Nair, Gokul G. Strogatz, Steven H. Parise, Francesca |
| author_facet | Nagpal, Shriya V. Nair, Gokul G. Strogatz, Steven H. Parise, Francesca |
| contents | 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 Erdős-Rényi random graphs. This result suggests a framework for studying synchronization properties in large but finite random networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13998 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Synchronization in random networks of identical phase oscillators: A graphon approach Nagpal, Shriya V. Nair, Gokul G. Strogatz, Steven H. Parise, Francesca Dynamical Systems Probability 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 Erdős-Rényi random graphs. This result suggests a framework for studying synchronization properties in large but finite random networks. |
| title | Synchronization in random networks of identical phase oscillators: A graphon approach |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2403.13998 |