Persistent Homology of Complex Networks for Dynamic State Detection

@article{Myers2019PersistentHO,
  title={Persistent Homology of Complex Networks for Dynamic State Detection},
  author={Audun D. Myers and E. Munch and Firas A. Khasawneh},
  journal={Physical review. E},
  year={2019},
  volume={100 2-1},
  pages={
          022314
        }
}
In this paper we develop an alternative topological data analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a compressed, multi-scale representation of the graph that can distinguish between dynamic states such as periodic and chaotic behavior. We show the approach for two graph constructions obtained from the time series. In the first approach the time series is… 

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