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arXiv · 2510.05243

Synchronization of coupled Stuart-Landau oscillators: How heterogeneity can facilitate synchronization

Ana P Millán·David Poyato·David N Reynolds·Francesco Tudisco
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Abstract

We study the collective dynamics of coupled Stuart--Landau oscillators, which model limit-cycle behavior near a Hopf bifurcation and serve as the amplitude-phase analogue of the Kuramoto model. Unlike the well-studied phase-reduced systems, the full Stuart--Landau model retains amplitude dynamics, enabling the emergence of rich phenomena such as amplitude death, quenching, and multistable synchronization. We provide a complete analytical classification of asymptotic behaviors for identical natural frequencies, but heterogeneous inherent amplitudes in the finite-$N$ setting. In the two-oscillator case, we classify the asymptotic behavior in all possible regimes including heterogeneous natural frequencies and inherent amplitudes, and in particular we identify and characterize a novel regime of \emph{leader-driven synchronization}, wherein one active oscillator can entrain another regardless of frequency mismatch. For general $N$, we prove exponential phase synchronization under sectorial initial data and establish sharp conditions for global amplitude death. Finally, we analyze a real-valued reduction of the model, connecting the dynamics to nonlinear opinion formation and consensus processes. Our results highlight the fundamental differences between amplitude-phase and phase-only Kuramoto models, and provide a new framework for understanding synchronization in heterogeneous oscillator networks.

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Ana P Millán, David Poyato, David N Reynolds, Francesco Tudisco. 2025-10-06. Synchronization of coupled Stuart-Landau oscillators: How heterogeneity can facilitate synchronization. https://arxiv.org/abs/2510.05243

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