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arXiv · 2609.02047

Phase-delays shape multistability and basin sizes in Kuramoto networks: analytical estimates from network structure

Kalel L. Rossi·Antonio Mihara·Lyle E. Muller·Rene O. Medrano-T·Roberto C. Budzinski
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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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Kalel L. Rossi, Antonio Mihara, Lyle E. Muller, Rene O. Medrano-T, Roberto C. Budzinski. 2026-09-02. Phase-delays shape multistability and basin sizes in Kuramoto networks: analytical estimates from network structure. https://arxiv.org/abs/2609.02047

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