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arXiv · 2606.16427

Criticality of nonreciprocal phase oscillators with long-range interactions

Minwoo Bae·Hiroshi Kori
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Abstract

We study noisy identical Kuramoto-Sakaguchi oscillators with phase lag $\alpha\in[0,\pi/2)$, where $\alpha>0$ induces nonreciprocal interactions. Numerical phase diagrams in the $(\sigma, \alpha)$ plane in fully-connected graphs, formed by long-range weights tuned by $\sigma$ on $d$-dimensional lattices, reveal a critical phase lag $\alpha_c$, below which spontaneous synchronization occurs. This critical phase lag decreases monotonically with $\sigma$. We characterize the critical behavior analytically using the dynamical renormalization group theory.

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Minwoo Bae, Hiroshi Kori. 2026-06-15. Criticality of nonreciprocal phase oscillators with long-range interactions. https://arxiv.org/abs/2606.16427

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