Phase-delays shape multistability and basin sizes in Kuramoto networks: analytical estimates from network structure
Abstract
We study how network connectivity and heterogeneous phase-delays shape the spatiotemporal dynamics of finite oscillator networks. Phase-delays can destabilize global synchronization and promote phase-locked patterns, including states with uniform phase gradients and more complex combinations of these modes. Yet, how connectivity and phase-delays jointly determine which states the network selects remains unclear. Here, we show that the spectrum of a composite matrix, which combines connectivity and phase-delays, governs not only the linear stability of the network's collective states but also their basin sizes. This, in turn, enables analytical estimates of basin size of phase-locked states for individual networks from connectivity and phase-delays alone. Applying this framework to nonlocal and global networks, including cases with random phase-delays, we uncover multistability and strong asymmetries in basin sizes, revealing chiral dynamics that conventional stability analysis cannot detect.
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BibTeX
@misc{rossi2026phasedelays,
title = {{Phase-delays shape multistability and basin sizes in Kuramoto networks: analytical estimates from network structure}},
author = {Kalel L. Rossi and Antonio Mihara and Lyle E. Muller and Rene O. Medrano-T and Roberto C. Budzinski},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02047},
eprint = {2609.02047},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02047},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Phase-delays shape multistability and basin sizes in Kuramoto networks: analytical estimates from network structure
AU - Kalel L. Rossi
AU - Antonio Mihara
AU - Lyle E. Muller
AU - Rene O. Medrano-T
AU - Roberto C. Budzinski
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02047
UR - https://arxiv.org/abs/2609.02047
AB - We study how network connectivity and heterogeneous phase-delays shape the spatiotemporal dynamics of finite oscillator networks. Phase-delays can destabilize global synchronization and promote phase-locked patterns, including states with uniform phase gradients and more complex combinations of these modes. Yet, how connectivity and phase-delays jointly determine which states the network selects remains unclear. Here, we show that the spectrum of a composite matrix, which combines connectivity and phase-delays, governs not only the linear stability of the network's collective states but also their basin sizes. This, in turn, enables analytical estimates of basin size of phase-locked states for individual networks from connectivity and phase-delays alone. Applying this framework to nonlocal and global networks, including cases with random phase-delays, we uncover multistability and strong asymmetries in basin sizes, revealing chiral dynamics that conventional stability analysis cannot detect.
ER -