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Higher-order interactions induce chimera states in globally coupled oscillators

Zerong Guo1, Zonghua Liu1, Shuguang Guan1,*, Charo I. del Genio2,3,4,†, Stefano Boccaletti3,5,6, and Jie Zhou1,‡

  • *Contact author: sgguan@phy.ecnu.edu.cn
  • †Contact author: charo.delgenio@trakia-uni.bg
  • ‡Contact author: jzhou@phy.ecnu.edu.cn
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Phys. Rev. Research 8, 023011 – Published 2 April, 2026

DOI: https://doi.org/10.1103/bq1t-y92y

Abstract

We show that globally coupled phase oscillators inherently possess a phase frustration when four-body interactions are considered. This intrinsic frustration arises when oscillators have asymmetric distributions of initial conditions spanning across multiple fixed points. Moreover, when the frequency distribution is bimodal, the two groups of oscillators may evolve toward distinct macroscopic dynamical behaviors, with one group being synchronized and the other remaining asynchronous. This constitutes a mechanism for the emergence of chimera states, and one that is specifically characteristic of higher-order interactions.

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References (56)

  1. J. M. Levine, J. Bascompte, P. B. Adler, and S. Allesina, Beyond pairwise mechanisms of species coexistence in complex communities, Nature (London) 546, 56 (2017).
  2. 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).
  3. M. Perc, J. J. Jordan, D. G. Rand, Z. Wang, S. Boccaletti, and A. Szolnoki, Statistical physics of human cooperation, Phys. Rep. 687, 1 (2017).
  4. U. Alvarez-Rodriguez, F. Battiston, G. Ferraz de Arruda, Y. Moreno, M. Perc, and V. Latora, Evolutionary dynamics of higher-order interactions in social networks, Nat. Hum. Behav. 5, 586 (2021).
  5. R. Sahasrabuddhe, L. Neuhäuser, and R. Lambiotte, Modelling non-linear consensus dynamics on hypergraphs, J. Phys. Complexity 2, 025006 (2021).
  6. E. Ganmor, R. Segev, and E. Schneidman, Sparse low-order interaction network underlies a highly correlated and learnable neural population code, Proc. Natl. Acad. Sci. USA 108, 9679 (2011).
  7. G. Petri, P. Expert, F. Turkheimer, R. Carhart-Harris, D. Nutt, P. J. Hellyer, and F. Vaccarino, Homological scaffolds of brain functional networks, J. R. Soc. Interface 11, 20140873 (2014).
  8. F. A. N. Santos, E. P. Raposo, M. D. Coutinho-Filho, M. Copelli, C. J. Stam, and L. Douw, Topological phase transitions in functional brain networks, Phys. Rev. E 100, 032414 (2019).
  9. A. R. Benson, R. Abebe, M. T. Schaub, A. Jadbabaie, and J. Kleinberg, Simplicial closure and higher-order link prediction, Proc. Natl. Acad. Sci. USA 115, 11221 (2018).
  10. 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).
  11. 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).
  12. 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).
  13. M. H. Matheny, J. Emenheiser, W. Fon, A. Chapman, A. Salova, M. Rohden, J. Li, M. Hudoba de Badyn, M. Pósfai, L. Duenas-Osorio, M. Mesbahi, J. P. Crutchfield, M. C. Cross, R. M. D’ Souza, and M. L. Roukes, Exotic states in a simple network of nanoelectromechanical oscillators, Science 363, eaav7932 (2019).
  14. Y. Zhang, V. Latora, and A. E. Motter, Unified treatment of synchronization patterns in generalized networks with higher-order, multilayer, and temporal interactions, Commun. Phys. 4, 195 (2021).
  15. S. Kundu and D. Ghosh, Higher-order interactions promote chimera states, Phys. Rev. E 105, L042202 (2022).
  16. X. Li, M. Small, and Y. Lei, Reservoir computing with higher-order interactive coupled pendulums, Phys. Rev. E 108, 064304 (2023).
  17. E. T. K. Mau, O. Omel’chenko, and M. Rosenblum, Phase reduction explains chimera shape: When multibody interaction matters, Phys. Rev. E 110, L022201 (2024).
  18. X. Ji and X. Li, Chimera-inspired dynamics: When higher-order interactions are expressed differently, Phys. Rev. E 110, 044204 (2024).
  19. D. M. Abrams and S. H. Strogatz, Chimera states for coupled oscillators, Phys. Rev. Lett. 93, 174102 (2004).
  20. F. Parastesh, S. Jafari, H. Azarnoush, Z. Shahriari, Z. Wang, S. Boccaletti, and M. Perc, Chimeras, Phys. Rep. 898, 1 (2021).
  21. S. W. Haugland, The changing notion of chimera states, a critical review, J. Phys. Complex. 2, 032001 (2021).
  22. C. R. Laing, Chimera states in heterogeneous networks, Chaos 19, 013113 (2009).
  23. C. R. Laing, The dynamics of chimera states in heterogeneous Kuramoto networks, Physica D 238, 1569 (2009).
  24. C. R. Laing, K. Rajendran, and I. G. Kevrekidis, Chimeras in random non-complete networks of phase oscillators, Chaos 22, 013132 (2012).
  25. M. R. Tinsley, S. Nkomo, and K. Showalter, Chimera and phase-cluster states in populations of coupled chemical oscillators, Nat. Phys. 8, 662 (2012).
  26. S. Nkomo, M. R. Tinsley, and K. Showalter, Chimera states in populations of nonlocally coupled chemical oscillators, Phys. Rev. Lett. 110, 244102 (2013).
  27. J. Shena, J. Hizanidis, V. Kovanis, and G. P. Tsironis, Turbulent chimeras in large semiconductor laser arrays, Sci. Rep. 7, 42116 (2017).
  28. T. Makinwa, K. Inaba, T. Inagaki, Y. Yamada, T. Leleu, T. Honjo, T. Ikuta, K. Enbutsu, T. Umeki, R. Kasahara, K. Aihara, and H. Takesue, Experimental observation of chimera states in spiking neural networks based on degenerate optical parametric oscillators, Commun. Phys. 6, 121 (2023).
  29. L. V. Gambuzza, A. Buscarino, S. Chessari, L. Fortuna, R. Meucci, and M. Frasca, Experimental investigation of chimera states with quiescent and synchronous domains in coupled electronic oscillators, Phys. Rev. E 90, 032905 (2014).
  30. T. Yamaguchi, Stacking fault and four-body interaction in the Si(111)7×7 structure, Phys. Rev. B 34, 1085 (1986).
  31. M. Horoi, Staggering of the nuclear charge radii in a superfluid model with good particle number, Phys. Rev. C 50, 2834 (1994).
  32. J. Han, Five-body van der Waals interactions, Phys. Rev. A 95, 062502 (2017).
  33. T. Tanaka and T. Aoyagi, Multistable attractors in a network of phase oscillators with three-body interactions, Phys. Rev. Lett. 106, 224101 (2011).
  34. C. Bick, P. Ashwin, and A. Rodrigues, Chaos in generically coupled phase oscillator networks with nonpairwise interactions, Chaos 26, 094814 (2016).
  35. P. S. Skardal and A. Arenas, Abrupt desynchronization and extensive multistability in globally coupled oscillator simplexes, Phys. Rev. Lett. 122, 248301 (2019).
  36. I. León and D. Pazó, Enlarged Kuramoto model: Secondary instability and transition to collective chaos, Phys. Rev. E 105, L042201 (2022).
  37. I. León, R. Muolo, S. Hata, and H. Nakao, Higher-order interactions induce anomalous transitions to synchrony, Chaos 34, 013105 (2024).
  38. P. Ashwin and A. Rodrigues, Hopf normal form with SN symmetry and reduction to systems of nonlinearly coupled phase oscillators, Physica D 325, 14 (2016).
  39. 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).
  40. 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).
  41. C. Mitra, A. Choudhary, S. Sinha, J. Kurths, and R. V. Donner, Multiple-node basin stability in complex dynamical networks, Phys. Rev. E 95, 032317 (2017).
  42. S. Khan and H. E. Türeci, Frequency combs in a lumped-element Josephson-junction circuit, Phys. Rev. Lett. 120, 153601 (2018).
  43. A. F. Taylor, P. Kapetanopoulos, B. J. Whitaker, R. Toth, L. Bull, and M. R. Tinsley, Clusters and switchers in globally coupled photochemical oscillators, Phys. Rev. Lett. 100, 214101 (2008).
  44. A. F. Taylor, M. R. Tinsley, F. Wang, and K. Showalter, Phase clusters in large populations of chemical oscillators, Angew. Chem. Int. Ed 50, 10161 (2011).
  45. A. Navas-Olive, M. Valero, T. Jurado-Parras, A. de Salas-Quiroga, R. G. Averkin, G. Gambino, E. Cid, and L. M. de la Prida, Multimodal determinants of phase-locked dynamics across deep-superficial hippocampal sublayers during theta oscillations, Nat. Commun. 11, 2217 (2020).
  46. A. Czurkó, J. Huxter, Y. Li, B. Hangya, and R. U. Muller, Theta phase classification of interneurons in the hippocampal formation of freely moving rats, J. Neurosci. 31, 2938 (2011).
  47. J. E. Quintero, S. J. Kuhlman, and D. G. McMahon, The biological clock nucleus: A multiphasic oscillator network regulated by light, J. Neurosci. 23, 8070 (2003).
  48. S. Ramans-Harborough, A. P. Kalverda, I. W. Manfield, G. S. Thompson, M. Kieffer, V. Uzunova, M. Quareshy, J. M. Prusinska, S. Roychoudhry, K.-I. Hayashi, R. Napier, C. del Genio, and S. Kepinski, Intrinsic disorder and conformational coexistence in auxin coreceptors, Proc. Natl. Acad. Sci. USA 120, e2221286120 (2023).
  49. E. Ott and T. M. Antonsen, Low dimensional behavior of large systems of globally coupled oscillators, Chaos 18, 037113 (2008).
  50. E. Ott and T. M. Antonsen, Long time evolution of phase oscillator systems, Chaos 19, 023117 (2009).
  51. E. A. Martens, E. Barreto, S. H. Strogatz, E. Ott, P. So, and T. M. Antonsen, Exact results for the Kuramoto model with a bimodal frequency distribution, Phys. Rev. E 79, 026204 (2009).
  52. H. Sakaguchi and Y. Kuramoto, A soluble active rotator model showing phase transitions via mutual entrainment, Prog. Theor. Phys. 76, 576 (1986).
  53. https://github.com/zrguo-complexnet/IntrinsicFrustration.
  54. P. Hagmann, L. Cammoun, X. Gigandet, R. Meuli, C. J. Honey, V. J. Wedeen, and O. Sporns, Mapping the structural core of human cerebral cortex, PLoS Biol. 6, e159 (2008).
  55. C. J. Honey, O. Sporns, L. Cammoun, X. Gigandet, J. P. Thiran, R. Meuli, and P. Hagmann, Predicting human resting-state functional connectivity from structural connectivity, Proc. Natl. Acad. Sci. USA 106, 2035 (2009).
  56. S. Huo, C. Tian, M. Zheng, S. Guan, C. Zhou, and Z. Liu, Spatial multi-scaled chimera states of cerebral cortex network and its inherent structure-dynamics relationship in human brain, Natl. Sci. Rev. 8, nwaa125 (2021).

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Phys. Rev. Research 8, 023011– Published 2 April, 2026
  • Received 2 June 2025
  • Revised 13 November 2025
  • Accepted 17 February 2026
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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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