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Complex network-based multistep forecasting model for hyperchaotic time series

Reshmi L. B.1,*, Drisya Alex Thumba1,†, K. Asokan2,‡, T. K. Manoj Kumar3,§, T. R. Ramamohan4,∥, and K. Satheesh Kumar3,¶

  • 1Department of Futures Studies, University of Kerala, Kariavattom, Kerala 695 581, India
  • 2Department of Mathematics, College of Engineering, Trivandrum, Kerala 695 016, India
  • 3Kerala University of Digital Sciences, Innovation and Technology (Digital University Kerala), Technopark Phase IV, Kerala 695317, India
  • 4Department of Chemical Engineering, M. S. Ramaiah Institute of Technology, MSR Nagar, Bangalore 560 054, India

  • *Contact author: reshmilb@keralauniversity.ac.in
  • †Contact author: drisyavictoria@gmail.com
  • ‡Contact author: asokank@cet.ac.in
  • §Contact author: manojtk@duk.ac.in
  • ∥Contact author: trr@msrit.edu
  • Contact author: satheesh.kumar@duk.ac.in
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Phys. Rev. E 110, 044302 – Published 3 October, 2024

DOI: https://doi.org/10.1103/PhysRevE.110.044302

Abstract

We present a method for predicting hyperchaotic time series using a complex network-based forecasting model. We first construct a network from a given time series, which serves as a coarse-grained representation of the underlying attractor. This network facilitates multistep forecasting by capturing the local nonlinearity of the dynamics and offers superior accuracy over more extended periods than traditional methods. The network is formed by converting the patterns of local oscillations into sequences of numerical symbols, which are then used to create nodes and edges in a network, capturing the system's dynamical behavior at a reduced resolution. The network allows predictions up to several steps ahead without the exponential error increase usually associated with linear first-order methods. The improved predictions result from the unique ability of the network to collect identical pattern transitions in the orbit dynamics into a system of neighborhoods in the network. The effectiveness of this approach is demonstrated through its application to several high-dimensional hyperchaotic systems, where it outperforms both the linear first-order and other network-based methods in terms of prediction accuracy and horizon. Besides enhancing the predictability of chaotic systems, this methodology also outlines a procedure to develop a discrete model flow within an attractor.

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References (57)

  1. M. Vogel, Contemp. Phys. 60, 271 (2019).
  2. B. Sivakumar, in Chaos in Hydrology: Bridging Determinism and Stochasticity (Springer, Netherlands, Dordrecht, 2017), pp. 149–171.
  3. E. Ott, Chaos in Dynamical Systems (Cambridge University Press, New York, 2002).
  4. R. Hegger, H. Kantz, and T. Schreiber, Chaos 9, 413 (1999).
  5. A. M. Anter and M. Ali, Soft Comput. 24, 1565 (2020).
  6. T. Ivancevic, L. Jain, J. Pattison, and A. Hariz, Nonlinear Dyn. 56, 23 (2009).
  7. M. U. Rehman, A. Shafique, K. H. Khan, S. Khalid, A. A. Alotaibi, T. Althobaiti, N. Ramzan, J. Ahmad, S. A. Shah, and Q. H. Abbasi, Sensors 22, 461 (2022).
  8. M. Lin, C. Huang, R. Chen, H. Fujita, and X. Wang, Complex Intell. Syst. 7, 1025 (2021).
  9. V. Gupta, M. Mittal, and V. Mittal, Analog Integrated Circuits Signal Process. 102, 479 (2020).
  10. V. Gupta, M. Mittal, and V. Mittal, Wireless Personal Commun. 118, 3615 (2021).
  11. M. Casdagli, Physica D 35, 335 (1989).
  12. H. Kantz and T. Schreiber, Nonlinear Time Series Analysis (Cambridge University Press, New York, 2003).
  13. Y. LeCun, Y. Bengio, and G. Hinton, Nature (London) 521, 436 (2015).
  14. A. Shinozaki, T. Miyano, and Y. Horio, Nonlinear Theory Appl., IEICE 11, 466 (2020).
  15. A. Sinozaki, K. Shiozawa, K. Kajita, T. Miyano, and Y. Horio, in 2019 International Joint Conference on Neural Networks (IJCNN) (IEEE, Piscataway, NJ, 2019), pp. 1–5.
  16. V. A. Gromov and E. Borisenko, Neural Comput. Appl. 26, 1827 (2015).
  17. M. N. Alemu, Int. J. Innovative Comput., Inf. Control 14, 1767 (2018).
  18. A. D. Pano-Azucena, E. Tlelo-Cuautle, B. Ovilla-Martinez, L. G. de la Fraga, and R. Li, J. Circuit. Syst. Comput. 30, 2150164 (2021).
  19. P. Ong and Z. Zainuddin, Appl. Soft Comput. 80, 374 (2019).
  20. D. Chen and W. Han, Complexity 18, 55 (2013).
  21. A. D. Pano-Azucena, E. Tlelo-Cuautle, S. X.-D. Tan, B. Ovilla-Martinez, and L. G. De la Fraga, Technologies 6, 90 (2018).
  22. J. Zhao, Y. Li, X. Yu, and X. Zhang, Discrete Dyn. Nat. Soc. 2014, 193758 (2014).
  23. M. Ardalani-Farsa and S. Zolfaghari, Neurocomputing 73, 2540 (2010).
  24. D. Li, M. Han, and J. Wang, IEEE Trans. Neural Netw. Learn. Syst. 23, 787 (2012).
  25. R. Chandra and M. Zhang, Neurocomputing 86, 116 (2012).
  26. M. Xu, M. Han, T. Qiu, and H. Lin, IEEE Trans. Cybern. 49, 2305 (2018).
  27. R. Chandra, Y.-S. Ong, and C.-K. Goh, Neurocomputing 243, 21 (2017).
  28. W. Guo, T. Xu, and Z. Lu, Neural Comput. Appl. 27, 883 (2016).
  29. B. Samanta, Expert Syst. Appl. 38, 11406 (2011).
  30. T. Feng, S. Yang, and F. Han, J. Vibroeng. 21, 1983 (2019).
  31. T. Zhongda, L. Shujiang, W. Yanhong, and S. Yi, Chaos, Solitons Fractals 98, 158 (2017).
  32. L.-y. Su, Comput. Math. Appl. 59, 737 (2010).
  33. X. Wu and Z. Song, Appl. Math. Comput. 219, 8584 (2013).
  34. W. Ma, J. Duan, W. Man, H. Zhao, and B. Chen, Eng. Appl. Artif. Intell. 58, 101 (2017).
  35. Y. Zhang, S. Bai, G. Lu, and X. Wu, Chin. J. Electron. 28, 127 (2019).
  36. M. Han, R. Zhang, and M. Xu, Neural Process. Lett. 46, 705 (2017).
  37. Y. Xiao, X. Xie, Q. Li, and T. Li, Physica A 525, 1259 (2019).
  38. Y.-Y. Fu, C.-J. Wu, J.-T. Jeng, and C.-N. Ko, Expert Syst. Appl. 37, 4441 (2010).
  39. S. Kurogi, M. Toidani, R. Shigematsu, and K. Matsuo, Neural Comput. Appl. 29, 341 (2018).
  40. M. Jokar, H. Salarieh, and A. Alasty, Chaos, Solitons Fractals 123, 373 (2019).
  41. Y. Li, X. Jiang, H. Zhu, X. He, S. Peeta, T. Zheng, and Y. Li, Nonlinear Dyn. 85, 179 (2016).
  42. Y. Wang, Z. Man, and L. Meihua, Int. J. Heat Technol. 38, 933 (2020).
  43. M. Mallika, K. Asokan, K. Kumar, T. Ramamohan, and K. S. Kumar, Pramana 95, 141 (2021).
  44. M. C. Mallika, S. Suriya Prabhaa, K. Asokan, K. S. Anil Kumar, T. R. Ramamohan, and K. S. Kumar, Phys. Rev. E 104, 054217 (2021).
  45. J. Zhang and M. Small, Phys. Rev. Lett. 96, 238701 (2006).
  46. Y. Yang and H. Yang, Physica A 387, 1381 (2008).
  47. Z. Gao and N. Jin, Phys. Rev. E 79, 066303 (2009).
  48. L. Lacasa, B. Luque, F. Ballesteros, J. Luque, and J. C. Nuno, Proc. Natl. Acad. Sci. USA 105, 4972 (2008).
  49. N. Marwan, J. F. Donges, Y. Zou, R. V. Donner, and J. Kurths, Phys. Lett. A 373, 4246 (2009).
  50. S. Mao and F. Xiao, IEEE Access 7, 40220 (2019).
  51. C. Wang, H. Zhang, W. Fan, and P. Ma, Energy 138, 977 (2017).
  52. M. Small, in 2013 IEEE International Symposium on Circuits and Systems (ISCAS) (IEEE, Piscataway, NJ, 2013), pp. 2509–2512.
  53. T. Sauer, J. A. Yorke, and M. Casdagli, J. Stat. Phys. 65, 579 (1991).
  54. T. Sauer and J. A. Yorke, Int. J. Bifurcation Chaos 03, 737 (1993).
  55. A. P. Kuznetsov and Y. V. Sedova, J. Appl. Nonlinear Dyn. 5, 161 (2016).
  56. Q. Yang and M. Bai, Nonlinear Dyn. 88, 189 (2017).
  57. L. Yi, W. Xiao, W. Yu, and B. Wang, J. Alg. Comput. Technol. 12, 361 (2018).

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Phys. Rev. E 110, 044302– Published 3 October, 2024
  • Received 31 March 2024
  • Accepted 12 August 2024
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