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Disputation Ariane Ernst

01.04.2025 | 10:00
Thema der Dissertation:
Mathematical modeling and analysis of neurotransmission
Thema der Disputation:
Synchronization of Kuramoto Oscillator
Abstract: Synchronization emerges in diverse natural contexts, from the flashing of fireflies to neuronal networks. Understanding how network structure influences this phenomenon remains a central challenge in dynamical systems. The Kuramoto model provides a powerful framework for studying this question, offering valuable insights despite its simple structure.
In this talk, we focus on the homogeneous case and explore structural conditions that guarantee global synchronization of Kuramoto oscillators on graphs, highlighting recent insights and open challenges. We begin by introducing the model, its gradient system formulation, and the concept of global synchronization. Next, starting from the well-known result for complete graphs, we examine connectivity as a sufficient condition for synchronization and review recently established bounds on the critical connectivity. We then shift our focus to the role of expansion, discussing a new result on global synchronization in expander graphs and its implications for Erdős–Rényi random graphs.

Zeit & Ort

01.04.2025 | 10:00

Seminarraum 2006
(Zuse-Institut Berlin, Takustr.7, 14195 Berlin)