Transforming Time Series into Complex Networks

We introduce transformations from time series data to the domain of complex networks which allow us to characterise the dynamics underlying the time series in terms of topological features of the complex network. We show that specific types of dynamics can be characterised by a specific prevalence in the complex network motifs. For example, low-dimensional chaotic flows with one positive Lyapunov exponent form a single family while noisy non-chaotic dynamics and hyper-chaos are both distinct. We find that the same phenomena is also true for discrete map-like data. These algorithms provide a new way of studying chaotic time series and equip us with a wide range of statistical measures previously not available in the field of nonlinear time series analysis.