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Identification and prediction of bifurcation tipping points using complex networks based on quasi-isometric mapping

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  • Peng, Xiaoyi
  • Zhao, Yi
  • Small, Michael

Abstract

Many models and real systems possess tipping points at which the state of the model or real system shifts dramatically. The ability to find any early-warnings in the vicinity of tipping points is of great importance to estimate how far the system is away from the critical point. Meanwhile, among the many schemes to convert time series into complex networks, the one-dimensional recurrence method has been proved to be a quasi-isometric mapping, and therefore retains geometric information. The quasi-isometric transformation method is adopted to discover underlying changes in systems. By measuring the characteristics of the resultant networks from time series, the changes in the system are captured. Furthermore, curve fitting is applied to expose the relation between the measures of networks and the distance between the parameter of the current state and the parameter at the tipping point for a given system. According to such relation, we can predict the vicinity of critical states hidden in the observational time series. This strategy is proven to be effective over a wide range of noise levels. One real electrocardiogram data-set and two real dynamical systems are employed to demonstrate the capability and reliability of the complex network method for identification of different exercise states and bifurcation behaviors.

Suggested Citation

  • Peng, Xiaoyi & Zhao, Yi & Small, Michael, 2020. "Identification and prediction of bifurcation tipping points using complex networks based on quasi-isometric mapping," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
  • Handle: RePEc:eee:phsmap:v:560:y:2020:i:c:s0378437120305781
    DOI: 10.1016/j.physa.2020.125108
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    1. Braga, A.C. & Alves, L.G.A. & Costa, L.S. & Ribeiro, A.A. & de Jesus, M.M.A. & Tateishi, A.A. & Ribeiro, H.V., 2016. "Characterization of river flow fluctuations via horizontal visibility graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 1003-1011.
    2. Damian Smug & Peter Ashwin & Didier Sornette, 2018. "Predicting financial market crashes using ghost singularities," PLOS ONE, Public Library of Science, vol. 13(3), pages 1-20, March.
    3. Sun, Mei & Wang, Yaqi & Gao, Cuixia, 2016. "Visibility graph network analysis of natural gas price: The case of North American market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1-11.
    4. Longfeng Zhao & Wei Li & Chunbin Yang & Jihui Han & Zhu Su & Yijiang Zou, 2017. "Multifractality and Network Analysis of Phase Transition," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-23, January.
    5. Ahmadi, Negar & Pei, Yulong & Pechenizkiy, Mykola, 2019. "Effect of linear mixing in EEG on synchronization and complex network measures studied using the Kuramoto model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 289-308.
    6. Yang, Yue & Yang, Huijie, 2008. "Complex network-based time series analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1381-1386.
    7. Long, Yu, 2013. "Visibility graph network analysis of gold price time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(16), pages 3374-3384.
    8. John M. Drake & Blaine D. Griffen, 2010. "Early warning signals of extinction in deteriorating environments," Nature, Nature, vol. 467(7314), pages 456-459, September.
    9. Ahmadlou, Mehran & Adeli, Hojjat & Adeli, Amir, 2012. "Improved visibility graph fractality with application for the diagnosis of Autism Spectrum Disorder," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4720-4726.
    10. Bezsudnov, I.V. & Snarskii, A.A., 2014. "From the time series to the complex networks: The parametric natural visibility graph," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 53-60.
    11. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.
    12. Vamvakaris, Michail D. & Pantelous, Athanasios A. & Zuev, Konstantin M., 2018. "Time series analysis of S&P 500 index: A horizontal visibility graph approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 41-51.
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    2. Tirabassi, Giulio & Masoller, Cristina, 2022. "Correlation lags give early warning signals of approaching bifurcations," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    3. Gangwal, Utkarsh & Singh, Mayank & Pandey, Pradumn Kumar & Kamboj, Deepak & Chatterjee, Samrat & Bhatia, Udit, 2022. "Identifying early-warning indicators of onset of sudden collapse in networked infrastructure systems against sequential disruptions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 591(C).

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