2015/05/01 by Michael McCullough, Michael Small, Thomas Stemler +1 · 3 citations
Computer Science · Physics and Astronomy · #Chaos control and synchronization #Neural Networks and Reservoir Computing #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.1063/1.4919075
openalex publication_date 2015/05/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31
We investigate a generalised version of the recently proposed ordinal partition time series to network transformation algorithm. First, we introduce a fixed time lag for the elements of each partition that is selected using techniques from traditional time delay embedding. The resulting partitions define regions in the embedding phase space that are mapped to nodes in the network space. Edges are allocated between nodes based on temporal succession thus creating a Markov chain representation of the time series. We then apply this new transformation algorithm to time series generated by the Rössler system and find that periodic dynamics translate to ring structures whereas chaotic time series translate to band or tube-like structures-thereby indicating that our algorithm generates networks whose structure is sensitive to system dynamics. Furthermore, we demonstrate that simple network measures including the mean out degree and variance of out degrees can track changes in the dynamical behaviour in a manner comparable to the largest Lyapunov exponent. We also apply the same analysis to experimental time series generated by a diode resonator circuit and show that the network size, mean shortest path length, and network diameter are highly sensitive to the interior crisis captured in this particular data set.