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  • Letter

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