Abstract
Recurrence networks are complex networks constructed from the time series of chaotic dynamical systems where the connection between two nodes is limited by the recurrence threshold. This condition makes the topology of every recurrence network unique with the degree distribution determined by the probability density variations of the representative attractor from which it is constructed. Here we numerically investigate the properties of recurrence networks from standard low-dimensional chaotic attractors using some basic network measures and show how the recurrence networks are different from random and scale-free networks. In particular, we show that all recurrence networks can cross over to random geometric graphs by adding sufficient amount of noise to the time series and into the classical random graphs by increasing the range of interaction to the system size. We also highlight the effectiveness of a combined plot of characteristic path length and clustering coefficient in capturing the small changes in the network characteristics.
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Acknowledgements
RJ and KPH acknowledge the financial support from Science and Engineering Research Board (SERB), Govt. of India in the form of a Research Project No. SR /S2 /HEP-27 /2012. KPH acknowledges the computing facilities in IUCAA, Pune.
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JACOB, R., HARIKRISHNAN, K.P., MISRA, R. et al. Cross over of recurrence networks to random graphs and random geometric graphs. Pramana - J Phys 88, 37 (2017). https://doi.org/10.1007/s12043-016-1339-y
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DOI: https://doi.org/10.1007/s12043-016-1339-y