New topological method detects Hopf bifurcations in time series data

Researchers have developed a novel topological framework to identify Hopf bifurcations directly from scalar time series data. This method combines delay-coordinate reconstruction with persistent homology, using the maximum persistence of one-dimensional homology classes as a descriptor for cyclic structures. The approach has been tested on various models, including the Hopf normal form, Lorenz system, and a reduced Belousov-Zhabotinsky model, demonstrating accurate localization of transitions and illustrating the impact of different parameters and data quality. AI

IMPACT Provides a new data-driven tool for analyzing geometric reorganizations in nonlinear time series, potentially applicable to complex systems.

RANK_REASON The cluster contains an academic paper detailing a new methodology for detecting dynamical transitions in time series data. [lever_c_demoted from research: ic=1 ai=0.4]

Read on arXiv stat.ML →

• arXiv
• Belousov--Zhabotinsky model
• Jhonathan Barrios
• Lorenz system
• persistent homology
• time series

• paper
• other

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