Characterization of chaotic attractors under noise: A recurrence network perspective

• Recurrence network measures are used for the first time to study how the white and colored noise added to a chaotic time series affects the structure of the underlying attractor.
• Though the addition of noise obscures the property of recurrence of the dynamical system, the structure of the attractor is found to be robust even upto high levels of noise contamination for both white and colored noise.
• Recurrence network measures are shown to be effective in identifying the nature of noise contamination in a real world data.

We undertake a detailed numerical investigation to understand how the addition of white and colored noise to a chaotic time series changes the topology and the structure of the underlying attractor reconstructed from the time series. We use the methods and measures of recurrence plot and recurrence network generated from the time series for this analysis. We explicitly show that the addition of noise obscures the property of recurrence of trajectory points in the phase space which is the hallmark of every dynamical system. However, the structure of the attractor is found to be robust even upto high noise levels of 50%. An advantage of recurrence network measures over the conventional nonlinear measures is that they can be applied on short and non stationary time series data. By using the results obtained from the above analysis, we go on to analyse the light curves from a dominant black hole system and show that the recurrence network measures are capable of identifying the nature of noise contamination in a time series.