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Multicircular static patterns in swarmalator systems: Radii and stability

Udo Schilcher, Marcus Schref, and Christian Bettstetter

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Phys. Rev. E 111, 064210 – Published 16 June, 2025

DOI: https://doi.org/10.1103/5912-s83l

Abstract

We analyze spatial patterns emerging in self-organized systems of swarmalators, focusing on constellations where all entities arrange in a sorted manner along one or more concentric circles. Key properties of these patterns are explored by computing their radii and examining stability criteria based on the number of entities and a coupling parameter. The findings can be applied to swarm robotics and other collective motion systems.

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References (39)

  1. S. Camazine, J.-L. Deneubourg, N. R. Franks, J. Sneyd, G. Theraulaz, and E. Bonabeau, Self-Organization in Biological Systems (Princeton University Press, Princeton, NJ, 2001).
  2. D. J. T. Sumpter, Collective Animal Behavior (Princeton University Press, Princeton, NJ, 2010).
  3. T. Vicsek and A. Zafeiris, Phys. Rep. 517, 71 (2012).
  4. T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, and O. Shochet, Phys. Rev. Lett. 75, 1226 (1995).
  5. J. Toner and Y. Tu, Phys. Rev. Lett. 75, 4326 (1995).
  6. G. Grégoire, H. Chaté, and Y. Tu, Physica D 181, 157 (2003).
  7. M. R. D'Orsogna, Y. L. Chuang, A. L. Bertozzi, and L. S. Chayes, Phys. Rev. Lett. 96, 104302 (2006).
  8. R. C. Fetecau, Y. Huang, and T. Kolokolnikov, Nonlinearity 24, 2681 (2011).
  9. R. Lukeman, Y.-X. Li, and L. Edelstein-Keshet, Proc. Natl. Acad. Sci. USA 107, 12576 (2010).
  10. J. E. Herbert-Read, A. Perna, R. P. Mann, T. M. Schaerf, D. J. T. Sumpter, and A. J. W. Ward, Proc. Natl. Acad. Sci. USA 108, 18726 (2011).
  11. K. P. O'Keeffe, H. Hong, and S. H. Strogatz, Nat. Commun. 8, 1504 (2017).
  12. Y. Dieudonné, O. Labbani-Igbida, and F. Petit, ACM Trans. Auton. Adapt. Syst. 3, 1 (2008).
  13. B. Rinner, C. Bettstetter, H. Hellwagner, and S. Weiss, IEEE Comput. 54, 34 (2021).
  14. A. Barciś, Synchronizing and swarming robots: Spatio-temporal coordination in multi-robot systems, Ph.D. thesis, University of Klagenfurt, Austria (2021).
  15. A. Barciś, M. Barciś, and C. Bettstetter, in Proc. of the International Symposium on Multi-Robot and Multi-Agent Systems (MRS) (MRS, New Brunswick, NJ, 2019), pp. 98–104.
  16. K. P. O'Keeffe, J. H. M. Evers, and T. Kolokolnikov, Phys. Rev. E 98, 022203 (2018).
  17. C. Bettstetter, Swarmalators: Static phase wave patterns (2025), https://youtube.com/watch?v=52myoGtzp1w.
  18. B. Hao, M. Zhong, and K. P. O'Keeffe, Phys. Rev. E 108, 064214 (2023).
  19. U. Schilcher, C. W. Rauter, and C. Bettstetter, in Proc. of the IEEE International Conference on Autonomic Computing and Self-Organizing Systems (ACSOS) (IEEE, New York, 2023), pp. 151–156.
  20. K. P. O'Keeffe, S. Ceron, and K. Petersen, Phys. Rev. E 105, 014211 (2022).
  21. S. Yoon, K. P. O'Keeffe, J. F. F. Mendes, and A. V. Goltsev, Phys. Rev. Lett. 129, 208002 (2022).
  22. H. Hong, K. P. O'Keeffe, J. S. Lee, and H. Park, Phys. Rev. Res. 5, 023105 (2023).
  23. M. S. Anwar, D. Ghosh, and K. P. O'Keeffe, Phys. Rev. E 110, 054205 (2024).
  24. J. U. F. Lizárraga and M. A. M. de Aguiar, Phys. Rev. E 108, 024212 (2023).
  25. Y. Lu, Y. Xu, W. Cai, Z. Tian, J. Xu, S. Wang, T. Zhu, Y. Liu, M. Wang, Y. Zhou, C. Yan, C. Li, and Z. Zheng, Chaos, Solitons Fractals 191, 115794 (2025).
  26. J. Delcourt, N. W. F. Bode, and M. Denoël, Q. Rev. Biol. 91, 1 (2016).
  27. C. Song, L. Liu, and S. Xu, IEEE Trans. Autom. Control 64, 2115 (2019).
  28. C. Wang and G. Xie, IEEE Trans. Autom. Control 62, 6560 (2017).
  29. G. S. Seyboth, J. Wu, J. Qin, C. Yu, and F. Allgöwer, IEEE Trans. Control Network Syst. 1, 167 (2014).
  30. I. Chatzigiannakis, M. Markou, and S. Nikoletseas, in Proc. of the International Workshop on Experimental and Efficient Algorithms (WEA) (Springer, Angra dos Reis, Brazil, 2004), pp. 159–174.
  31. Y. Lan, G. Yan, and Z. Lin, Syst. Control Lett. 59, 381 (2010).
  32. A. Barciś and C. Bettstetter, IEEE Access 8, 218752 (2020).
  33. S. Ceron, G. Gardi, K. Petersen, and M. Sitti, Proc. Natl. Acad. Sci. USA 120, e2221913120 (2023).
  34. S. Ceron, W. Xiao, and D. Rus, in Proc. of the IEEE International Conference on Robotics and Automation (ICRA) (IEEE, New York, 2024), pp. 12233–12239.
  35. A. Peshkov, S. McGaffigan, and A. C. Quillen, Soft Matter 18, 1174 (2022).
  36. I. Aihara, Sci. Rep. 4, 3891 (2014).
  37. A. Yadav, K. J, V. K. Chandrasekar, W. Zou, J. Kurths, and D. V. Senthilkumar, Phys. Rev. E 109, 044212 (2024).
  38. https://www.fwf.ac.at/en/research-radar/10.55776/P30012.
  39. U. Schilcher and M. Schref, Raw data of all figures within this article (2025), https://mobile.aau.at/swarmalators/data/circ.html.

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Phys. Rev. E 111, 064210– Published 16 June, 2025
  • Received 19 February 2025
  • Accepted 12 May 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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