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Strong asymmetric multicluster synchrony in globally coupled simplicial complexes

Zongkai Cai1, Shuguang Guan1, Jürgen Kurths2, and Yong Zou1

  • Contact author: sgguan@phy.ecnu.edu.cn
  • Contact author: yzou@phy.ecnu.edu.cn
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Phys. Rev. Research 7, 043136 – Published 5 November, 2025

DOI: https://doi.org/10.1103/ycxn-l2l3

Abstract

In recent years, the investigation of synchronization in higher-order networks has emerged as a prominent area of research in nonlinear dynamics. In this work, we present a substantially generalized model of phase oscillators on globally coupled simplex structures that elucidate the formation mechanisms of strongly asymmetric synchronization clusters in complex systems characterized by many-body interactions. The strong asymmetric cluster synchrony involves three characteristics: (1) each cluster shows a different frequency band for the natural frequencies of the synchronized oscillators, (2) the phases of each cluster are locked to different interval sizes, and (3) the oscillators are nonuniformly distributed between the clusters. Focusing on a paradigmatic example of two coupled 2-simplex (three-body) interactions, we use the mean-field method to identify the existence of strongly asymmetric multicluster synchrony. Their solutions are analytically obtained through self-consistent equations. Our results also demonstrate, both theoretically and numerically, that the presence of asymmetric multicluster synchrony gives rise to multistability. When increasing the coupling strength, the system shows a transition to synchronization, which is then followed by synchronization fading, a complete loss of synchronization, and synchronization re-establishment. Our findings are not only limited to this case, but can also be extended to n-simplex interactions. Furthermore, we highlight that the inclusion of two-body interaction terms can disrupt the stability of the incoherent state, inducing spontaneous synchronization.

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References (38)

  1. C. Bick, E. Gross, H. A. Harrington, and M. T. Schaub, What are higher-order networks? SIAM Rev. 65, 686 (2023).
  2. F. Battiston, G. Cencetti, I. Iacopini, V. Latora, M. Lucas, A. Patania, J.-G. Young, and G. Petri, Networks beyond pairwise interactions: Structure and dynamics, Phys. Rep. 874, 1 (2020).
  3. S. Boccaletti, P. De Lellis, C.I. del Genio, K. Alfaro-Bittner, R. Criado, S. Jalan, and M. Romance, The structure and dynamics of networks with higher order interactions, Phys. Rep. 1018, 1 (2023).
  4. H. Sun, F. Radicchi, J. Kurths, and G. Bianconi, The dynamic nature of percolation on networks with triadic interactions, Nat. Commun. 14, 1308 (2023).
  5. E. Bairey, E. D. Kelsic, and R. Kishony, High-order species interactions shape ecosystem diversity, Nat. Commun. 7, 12285 (2016).
  6. J. Grilli, G. Barabás, M. J. Michalska-Smith, and S. Allesina, Higher-order interactions stabilize dynamics in competitive network models, Nature (London) 548, 210 (2017).
  7. U. Alvarez-Rodriguez, F. Battiston, G. F. de Arruda, Y. Moreno, M. Perc, and V. Latora, Evolutionary dynamics of higher-order interactions in social networks, Nat. Hum. Behav. 5, 586 (2020).
  8. A. P. Millán, H. Sun, L. Giambagli, R. Muolo, T. Carletti, J. J. Torres, F. Radicchi, J. Kurths, and G. Bianconi, Topology shapes dynamics of higher-order networks, Nat. Phys. 21, 353 (2025).
  9. P. S. Skardal and A. Arenas, Abrupt desynchronization and extensive multistability in globally coupled oscillator simplexes, Phys. Rev. Lett. 122, 248301 (2019).
  10. C. Xu, X. Wang, and P. S. Skardal, Bifurcation analysis and structural stability of simplicial oscillator populations, Phys. Rev. Res. 2, 023281 (2020).
  11. X. Wang, Z. Zheng, and C. Xu, Collective dynamics of phase oscillator populations with three-body interactions, Phys. Rev. E 104, 054208 (2021).
  12. P. S. Skardal and A. Arenas, Higher order interactions in complex networks of phase oscillators promote abrupt synchronization switching, Commun. Phys. 3, 218 (2020).
  13. K. Kovalenko, X. Dai, K. Alfaro-Bittner, A. M. Raigorodskii, M. Perc, and S. Boccaletti, Contrarians synchronize beyond the limit of pairwise interactions, Phys. Rev. Lett. 127, 258301 (2021).
  14. C. Xu and P. S. Skardal, Spectrum of extensive multiclusters in the Kuramoto model with higher-order interactions, Phys. Rev. Res. 3, 013013 (2021).
  15. N. G. Sabhahit, A. S. Khurd, and S. Jalan, Prolonged hysteresis in the Kuramoto model with inertia and higher-order interactions, Phys. Rev. E 109, 024212 (2024).
  16. A. Sharma, P. Rajwani, and S. Jalan, Synchronization transitions in adaptive Kuramoto–Sakaguchi oscillators with higher-order interactions, Chaos 34, 081103 (2024).
  17. 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).
  18. G. S. Costa, M. Novaes, and M. A. M. de Aguiar, Bifurcations in the Kuramoto model with external forcing and higher-order interactions, Chaos 34, 123133 (2024).
  19. C. Bick, T. Böhle, and O. E. Omel'chenko, Hopf bifurcations of twisted states in phase oscillators rings with nonpairwise higher-order interactions, J. Phys.: Complexity 5, 025026 (2024).
  20. Y. Zhang, P. S. Skardal, F. Battiston, G. Petri, and M. Lucas, Deeper but smaller: Higher-order interactions increase linear stability but shrink basins, Sci. Adv. 10, eado8049 (2024).
  21. 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).
  22. L. D. Smith and P. Liu, Determining bifurcations to explosive synchronization for networks of coupled oscillators with higher-order interactions, Phys. Rev. E 109, L022202 (2024).
  23. G. S. Costa, M. Novaes, and M. A. M. de Aguiar, Exact solutions of the Kuramoto model with asymmetric higher order interactions of arbitrary order, Chaos, Solitons Fractals 195, 116243 (2025).
  24. Y. Marui and H. Kori, Synchronization and its slow decay in noisy oscillators with simplicial interactions, Phys. Rev. E 111, 014223 (2025).
  25. P. S. Skardal, E. Ott, and J. G. Restrepo, Cluster synchrony in systems of coupled phase oscillators with higher-order coupling, Phys. Rev. E 84, 036208 (2011).
  26. M. Banaji, Strongly asymmetric clustering in systems of phase oscillators, Phys. Rev. E 71, 016212 (2005).
  27. M. Komarov and A. Pikovsky, Multiplicity of singular synchronous states in the Kuramoto model of coupled oscillators, Phys. Rev. Lett. 111, 204101 (2013).
  28. M. Komarov and A. Pikovsky, The Kuramoto model of coupled oscillators with a bi-harmonic coupling function, Phys. D 289, 18 (2014).
  29. Z. Cai, Z. Liu, S. Guan, J. Kurths, and Y. Zou, High-mode coupling yields multicoherent-phase phenomena in nonlocally coupled oscillators, Phys. Rev. Lett. 133, 227201 (2024).
  30. M. H. Matheny, J. Emenheiser, W. Fon, A. Chapman, A. Salova, M. Rohden, J. Li, M. H. De Badyn, M. Posfai, and L. Duenas-Osorio, Exotic states in a simple network of nanoelectromechanical oscillators, Science 363, eaav7932 (2019).
  31. E. Gengel, E. Teichmann, M. Rosenblum, and A. Pikovsky, High-order phase reduction for coupled oscillators, J. Phys. Complexity 2, 015005 (2021).
  32. I. León and D. Pazó, Enlarged Kuramoto model: Secondary instability and transition to collective chaos, Phys. Rev. E 105, L042201 (2022).
  33. E. T. K. Mau, M. Rosenblum, and A. Pikovsky, High-order phase reduction for coupled 2D oscillators, Chaos 33, 101101 (2023).
  34. E. T. K. Mau, O. E. Omel'chenko, and M. Rosenblum, Phase reduction explains chimera shape: When multibody interaction matters, Phys. Rev. E 110, L022201 (2024).
  35. Y. Park and D. Wilson, N-body oscillator interactions of higher-order coupling functions, SIAM J. Appl. Dyn. Syst. 23, 1471 (2024).
  36. E. Ott and T. M. Antonsen, Low dimensional behavior of large systems of globally coupled oscillators, Chaos 18, 037113 (2008).
  37. Z. Chen, Z. Zheng, and C. Xu, Phase transitions of coupled oscillators with mixed higher-order interactions, Phys. Rev. E 112, 014224 (2025).
  38. S. H. Strogatz and R. E. Mirollo, Stability of incoherence in a population of coupled oscillators, J. Stat. Phys. 63, 613 (1991).

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Phys. Rev. Research 7, 043136– Published 5 November, 2025
  • Received 23 April 2025
  • Accepted 3 October 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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