Detecting Bifurcations in Dynamical Systems with Zigzag Persistent Homology

Explore a 24-minute conference talk on detecting bifurcations in dynamical systems using zigzag persistent homology. Learn about a novel one-step method that captures topological changes in the state space of dynamical systems through a single persistence diagram. Discover how this approach improves upon standard persistent homology techniques, which often require analyzing multiple persistence diagrams and increase computational costs. Gain insights into the importance of identifying parameter values for bifurcations in understanding overall system behavior. Follow the presentation's structure, covering topics such as persistent homology basics, persistence modules and diagrams, ordered point clouds, data generation, and practical examples of zigzag persistence application.

Introduction
What is persistent homology
Persistence module
Persistence diagram
Ordered point clouds
Example
Generating the data
Zig Zag example
Zig Zag persistence diagram
Questions
Wrapup