Tracking Dynamical Transitions using Link Density of Recurrence Networks

Abstract: We present Link Density (LD) computed from the Recurrence Network (RN) of a time series data as an effective measure that can detect dynamical transitions in a system. We illustrate its use using time series from the standard Rossler system in the period doubling transitions and the transition to chaos. Moreover, we find that the standard deviation of LD can be more effective in highlighting the transition points. We also consider the variations in data when the parameter of the system is varying due to internal or intrinsic perturbations but at a time scale much slower than that of the dynamics. In this case also, the measure LD and its standard deviation correctly detect transition points in the underlying dynamics of the system. The computation of LD requires minimal computing resources and time, and works well with short data sets. Hence, we propose this measure as a tool to track transitions in dynamics from data, facilitating quicker and more effective analysis of large number of data sets.