Regensburg 2025 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 34: Nonlinear Dynamics, Synchronization, and Chaos

DY 34.1: Talk

Thursday, March 20, 2025, 11:30–11:45, H43

Hierarchical Clustering in Mean-Field Coupled Stuart-Landau Oscillators — •Nicolas Thomé and Katharina Krischer — Technische Universität München

Coupled oscillator networks are fundamental in many physics, chemistry, and biology fields, representing a captivating subject of study in nonlinear science. A persistent challenge is understanding the transition from a coherent synchronous solution to a completely incoherent one. This work explores this transition using globally coupled Stuart-Landau oscillators under mean-field interactions. We show that a cascade of codimension-2 points, coined Type-II cluster singularities, organizes the transition from two- to three-cluster solutions. These Type-II cluster singularities naturally induce a hierarchal structure to the clustering behavior and pave the way for the formation of chimera and incoherent solutions. Based on numerical bifurcation and Floquet multiplier analyses, our findings offer new insights into intermediate synchronization states and their role in complex oscillator systems.

Keywords: Coupled Stuart Landau Oscillators; Numerical Bifurcation Analysis; Hierarchial Clustering