Bifurcation Analysis using Zigzag Persistence

Sarah Tymochko, Elizabeth Munch, Firas Khasawneh

Keywords: topological data analysis, time series analysis, zigzag persistence

TL;DR: We develop a novel method of using zigzag persistence to detect Hopf bifurcations in dynamical systems.

Abstract: As bifurcations in a dynamical system are drastic behavioral changes, being able to detect when these bifurcations occur can be essential to understanding the system overall. While persistent homology has successfully been used in the field of dynamical systems, the most commonly used approaches have their limitations. Using zigzag persistence, we can simplify the methodology and capture topological changes through a collection of time series, rather that studying the topology of individual time series separately. Here we present Bifurcations using ZigZag (BuZZ), a method to detect Hopf bifurcations in dynamical systems.

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