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  • Letter
  • Open Access

Double explosive Kuramoto transition in hypergraphs

Sangita Dutta1,*, Prosenjit Kundu2, Pitambar Khanra3, Ludovico Minati4,5,†, Stefano Boccaletti6,7,8, Pinaki Pal1,‡, and Chittaranjan Hens9

  • *Contact author: sangitaduttaprl@gmail.com
  • †Contact author: lminati@uestc.edu.cn; lminati@ieee.org
  • ‡Contact author: ppal.maths@nitdgp.ac.in
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Phys. Rev. Research 7, L022049 – Published 2 June, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L022049

Abstract

This study aims to develop a generalized concept that will enable double explosive transitions in the forward and backward directions or a combination thereof. We found two essential factors for generating such phase transitions: the use of higher-order (triadic) interactions and the partial adaptation of a global order parameter acting on the triadic coupling. A compromise between the two factors may result in a double explosive transition. To reinforce numerical observations, we employed the Ott-Antonsen ansatz. We observed that for a wide class of hypergraphs, combining two elements can result in a double explosive transition.

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References (47)

  1. M. Newman, Networks: An Introduction (Oxford University Press, Oxford, UK, 2010).
  2. P. Erdős and A. Rényi, On random graphs I, Publ. Math. Debrecen 6, 290 (1959).
  3. M. Li, R.-R. Liu, L. Lü, M.-B. Hu, S. Xu, and Y.-C. Zhang, Percolation on complex networks: Theory and application, Phys. Rep. 907, 1 (2021).
  4. D. Achlioptas, R. M. D'Souza, and J. Spencer, Explosive percolation in random networks, Science 323, 1453 (2009).
  5. O. Riordan and L. Warnke, Explosive percolation is continuous, Science 333, 322 (2011).
  6. J. Nagler, T. Tiessen, and H. W. Gutch, Continuous percolation with discontinuities, Phys. Rev. X 2, 031009 (2012).
  7. R. M. D'Souza and J. Nagler, Anomalous critical and supercritical phenomena in explosive percolation, Nat. Phys. 11, 531 (2015) .
  8. O. Riordan and L. Warnke, Achlioptas processes are not always self-averaging, Phys. Rev. E 86, 011129 (2012).
  9. S. Boccaletti, G. Bianconi, R. Criado, C. I. Del Genio, J. Gómez-Gardenes, M. Romance, I. Sendina-Nadal, Z. Wang, and M. Zanin, The structure and dynamics of multilayer networks, Phys. Rep. 544, 1 (2014).
  10. F. A Rodrigues, T. K. DM. Peron, P. Ji, and J. Kurths, The Kuramoto model in complex networks, Phys. Rep. 610, 1 (2016).
  11. Y. Kuramoto, Chemical Turbulence (Springer, Berlin, 1984).
  12. P. Kundu, C. Hens, B. Barzel, and P. Pal, Perfect synchronization in networks of phase-frustrated oscillators, Europhys. Lett. 120, 40002 (2017).
  13. M. Zanin, D. Papo, P. A. Sousa, E. Menasalvas, A. Nicchi, E. Kubik, and S. Boccaletti, Combining complex networks and data mining: why and how, Phys. Rep. 635, 1 (2016).
  14. T. Ichinomiya, Frequency synchronization in a random oscillator network, Phys. Rev. E 70, 026116 (2004).
  15. B. C. Coutinho, A. V. Goltsev, S. N. Dorogovtsev, and J. F. F. Mendes, Kuramoto model with frequency-degree correlations on complex networks, Phys. Rev. E 87, 032106 (2013).
  16. J. Gómez-Gardenes, S. Gómez, A. Arenas, and Y. Moreno, Explosive synchronization transitions in scale-free networks, Phys. Rev. Lett. 106, 128701 (2011).
  17. T. Qiu, Y. Zhang, J. Liu, H. Bi, S Boccaletti, Z. Liu, and S. Guan, Landau damping effects in the synchronization of conformist and contrarian oscillators, Sci. Rep. 5, 18235 (2015).
  18. X. Zhang, S. Boccaletti, S. Guan, and Z. Liu, Explosive synchronization in adaptive and multilayer networks, Phys. Rev. Lett. 114, 038701 (2015).
  19. M. Manoranjani, V. R. Saiprasad, R. Gopal, D. V. Senthilkumar, and V. K. Chandrasekar, Phase transitions in an adaptive network with the global order parameter adaptation, Phys. Rev. E 108, 044307 (2023).
  20. G. Filatrella, N. F. Pedersen, and K. Wiesenfeld, Generalized coupling in the Kuramoto model, Phys. Rev. E 75, 017201 (2007).
  21. P. Khanra, P. Kundu, P. Pal, P. Ji, and C. Hens, Amplification of explosive width in complex networks, Chaos 30, 031101 (2020).
  22. P. Khanra and P. Pal, Explosive synchronization in multilayer networks through partial adaptation, Chaos, Solitons Fractals 143, 110621 (2021).
  23. D. Biswas and S. Gupta, Effect of adaptation functions and multilayer topology on synchronization, Phys. Rev. E 109, 024221 (2024).
  24. P. Kundu and P. Pal, Synchronization transition in Sakaguchi-Kuramoto model on complex networks with partial degree-frequency correlation, Chaos 29, 013123 (2019).
  25. S. Olmi, A. Navas, S. Boccaletti, and A. Torcini, Hysteretic transitions in the Kuramoto model with inertia, Phys. Rev. E 90, 042905 (2014).
  26. J. Gao and K. Efstathiou, Synchronized clusters in globally connected networks of second-order oscillators: Uncovering the role of inertia, Chaos 31, 093137 (2021).
  27. A. Carballosa, A. P. Muñuzuri, S. Boccaletti, A. Torcini, and S. Olmi, Cluster states and π-transition in the Kuramoto model with higher order interactions, Chaos, Solitons Fractals 177, 114197 (2023).
  28. J. Fialkowski, S. Yanchuk, I. M. Sokolov, E. Schöll, G. A. Gottwald, and R. Berner, Heterogeneous nucleation in finite-size adaptive dynamical networks, Phys. Rev. Lett. 130, 067402 (2023).
  29. A. Seif and M. Zarei, Double hysteresis loop in synchronization transitions of multiplex networks: The role of frequency arrangements and frustration, Chaos, Solitons & Fractals 196, 116412 (2025).
  30. O. T. Courtney and G. Bianconi, Generalized network structures: The configuration model and the canonical ensemble of simplicial complexes, Phys. Rev. E 93, 062311 (2016).
  31. N. W. Landry and J. G. Restrepo, The effect of heterogeneity on hypergraph contagion models, Chaos 30, 103117 (2020).
  32. P. S. Skardal and A. Arenas, Higher order interactions in complex networks of phase oscillators promote abrupt synchronization switching, Commun. Phys. 3, 218 (2020).
  33. P. S. Skardal and C. Xu, Tiered synchronization in coupled oscillator populations with interaction delays and higher-order interactions, Chaos 32, 053120 (2022).
  34. A. Suman and S. Jalan, Finite-size effect in Kuramoto oscillators with higher-order interactions, Chaos 34, 101101 (2024).
  35. S. Dutta, P. Kundu, P. Khanra, C. Hens, and P. Pal, Perfect synchronization in complex networks with higher-order interactions, Phys. Rev. E 108, 024304 (2023).
  36. S. Dutta, A. Mondal, P. Kundu, P. Khanra, P. Pal, and C. Hens, Impact of phase lag on synchronization in frustrated Kuramoto model with higher-order interactions, Phys. Rev. E 108, 034208 (2023).
  37. S. Dutta, P. Kundu, P. Khanra, C. Hens, and P. Pal, Transition to synchronization in the adaptive Sakaguchi-Kuramoto model with higher-order interactions, Phys. Rev. E 110, 064317 (2024).
  38. M. S. Anwar, S. N. Jenifer, P. Muruganandam, D. Ghosh, and T. Carletti, Synchronization in adaptive higher-order networks, Phys. Rev. E 110, 064305 (2024).
  39. M. S. Anwar, N. Frolov, A. E. Hramov, and D. Ghosh, Self-organized bistability on globally coupled higher-order networks, Phys. Rev. E 109, 014225 (2024).
  40. R. Ghosh, Md S. Anwar, D. Ghosh, J. Kurths, and M. D. Shrimali, Transitions to synchronization in adaptive multilayer networks with higher-order interactions, arXiv:2501.12301.
  41. E. Ott and T. M. Antonsen, Low dimensional behavior of large systems of globally coupled oscillators, Chaos 18, 037113 (2008).
  42. H. Sakaguchi and Y. Kuramoto, A soluble active rotater model showing phase transitions via mutual entertainment, Prog. Theor. Phys. 76, 576 (1986).
  43. P. Kundu, P. Khanra, C. Hens, and P. Pal, Transition to synchrony in degree-frequency correlated Sakaguchi-Kuramoto model, Phys. Rev. E 96, 052216 (2017).
  44. O. E. Omel'chenko and M. Wolfrum, Nonuniversal transitions to synchrony in the sakaguchi-kuramoto model, Phys. Rev. Lett. 109, 164101 (2012).
  45. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.7.L022049 for the construction of hypergraphs, the derivation and analysis of the self-consistent equations for degree-correlated networks and random network, the synchronization transitions for partial order parameter adaptation with the pairwise coupling, the frequency evolution of nodes during different kinds of synchronization transitions.
  46. S. Adhikari, J. G. Restrepo, and P. S. Skardal, Synchronization of phase oscillators on complex hypergraphs, Chaos 33, 033116 (2023).
  47. P. Rajwani, A. Suman, and S. Jalan, Tiered synchronization in Kuramoto oscillators with adaptive higher-order interactions, Chaos 33, 061102 (2023).

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Information

Phys. Rev. Research 7, L022049– Published 2 June, 2025
  • Received 30 December 2024
  • Accepted 8 April 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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