Phase space visibility graph

We introduce a topological approach for quantifying the dynamical complexity of time series. A novel complex network of visibility graph family is proposed based on defining visibility algorithm in phase space. The statistical properties of the constructed network show powerful potentiality for distinguishing stochastic and chaotic systems. And for some remarkable chaotic systems, it allows for quantitative correspondence with Lyapunov exponents. The potential practical application of this approach is demonstrated on the multiphase flow system and bearing fault identification. This work paves a natural way constructing complex network in phase space, and provides a complexity quantitative estimate for chaotic time series.

Automated summary

In this study, a topological approach is introduced to quantify the dynamical complexity of time series. A novel complex network of visibility graph family is proposed based on defining visibility algorithm in phase space. The statistical properties of the constructed network show powerful potentiality for distinguishing stochastic and chaotic systems. For some remarkable chaotic systems, it allows for quantitative correspondence with Lyapunov exponents. The potential practical application of this approach is demonstrated on the multiphase flow system and bearing fault identification.