WIAS Preprint No. 3186, (2025)

Hierarchical clustering in mean-field coupled Stuart--Landau oscillators


Authors

  • Thomè, Nicolas
  • Wolfrum, Matthias
    ORCID: 0000-0002-4278-2675
  • Krischer, Katharina

2020 Mathematics Subject Classification

  • 37G40 34C15

Keywords

  • Coupled oscillators, pattern formation, cluster dynamics, equivariant bifurcations

DOI

10.20347/WIAS.PREPRINT.3186

Abstract

Clustered solutions in oscillator networks provide an important insight into how a system might diversify from a synchronous solution into spatiotemporal complex solutions. They can therefore form a link between fully synchronized and incoherent states. Despite their fundamental role in coupled oscillator dynamics, our understanding of how these clusters form and differentiate is still quite limited. Here, we study an ensemble of globally coupled Stuart--Landau oscillators and focus on the question of how 3-cluster solutions emerge from 2-cluster solutions and how the different 3-cluster solutions are organized in parameter space. We show that the arrangement of the clusters is dictated by a co-dimension 2 point, which we coin Type-II cluster singularity. Furthermore, our study points to a hierarchical structure of higher cluster solutions.

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