Regensburg 2025 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 27: Poster: Nonlinear Dynamics, Pattern Formation, Granular Matter

DY 27.5: Poster

Wednesday, March 19, 2025, 15:00–18:00, P4

Origin of Frequency Clusters in Globally Coupled Phase Oscillators — •Yannick Schöhs, Nicolas Thomé, and Katharina Krischer — Technische Universität München

Frequency clusters arise in a wide range of physical, technological, and biological systems, making them a topic of significant interest both for their practical implications and for advancing the fundamental understanding of collective dynamics. Despite their importance, their origin remains relatively unexplored. In this study, we investigate the origin of frequency clusters using a model of globally coupled phase oscillators with adaptive coupling strength. By numerically solving the differential equations for a network of 100 oscillators, the formation of up to four distinct frequency clusters was confirmed. Additionally, we conducted a bifurcation analysis on a system of four oscillators. The reduced system size allowed for an analytical bifurcation analysis of the fixed points, while the bifurcation analysis of the limit cycles was performed numerically. The results reveal that the frequency clusters originate from a homoclinic bifurcation and lose their stability through a transcritical bifurcation.

Keywords: Frequency Clusters; Adaptively Coupled Phase Oscillators; Analytical and Numerical Bifurcation Analysis