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

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- 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 , 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.

Please cite this paper as:

@article{millan2025synchronization,
  title={Synchronization of coupled Stuart-Landau oscillators: How heterogeneity can facilitate synchronization},
  author={Mill{\'a}n, Ana P and Poyato, David and Reynolds, David N and Tudisco, Francesco},
  journal={arXiv preprint arXiv:2510.05243},
  year={2025}
}

Keywords: Stuart-Landau oscillators synchronization dynamical systems heterogeneous networks collective dynamics