Synchronization in Swarmalators Systems: the XY Model

Hilda A. Cerdeira

Instituto de Física Teórica

IFT – UNESP

São Paulo, BRAZIL

Medyfinol – 8 December 2022 Colonia del Sacramento, Uruguay

Collaborators

Steve Kongni

Thierry Njougouo

Patrick Louodop

Robert Tchitnga

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What are swarmalators?

Swarmalators is a system of oscillators whose phase and spatial dynamics are coupled and they are used to describe the dynamics of living systems

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The Model

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We study the effect that the internal dynamics has on the spatial distribution of the swarmalators, and vice-versa. We find that the expected explosive synchronization is not a necessary characteristic of the system.

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a) Static Async; b) Static Phase Wave; c) Active Phase Wave; d) Splintered Phase Wave; e) Static Sync

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Near synchronization the distance between swarmalators is practically constant and the energy can be approximated by:

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Explosive or non Explosive Synchronization?

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a) According to D. Pazó the Kuramoto model has a first order first transition from incoherence to synchronization in the thermodynamic limit, provided the natural frequencies are evenly spaced or uniformly distributed in a finite range.�b) Gomez Gardeñes et al. have shown that there is an explosive transition in a scale free network of Kuramoto oscillators when the natural frequency and the degree of a node are equal.�c) Skardal et al. observed that adding infinitesimal disorder induces explosive transition to synchronization for the case discussed in (b).�d) Hong and Martens studied phase transitions in an XY model related to a variant of the Kuramoto model for coupled oscillators. They found that for the case without noise, the system shows features of a first-order phase transition at complete synchronization, while this transition is found to be continuous for the noisy case.

D. Pazó, Phys. Ver. E 72, 046211 (2005).�J. Gómez-Gardeñes, S. Gómez, A. Arenas, and Y. Moreno, Phys. Rev. Lett. 106, 128701 (2011).�P. S. Skardal and A. Arenas, Phys. Ver. E 89, 062811 (2014).�H. Hong and E. A. Martens, Chaos 32, 063125 (2022).

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Left: Equal natural frequencies. Right: Frequencies randomly distributed.

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Random distribution of natural frequencies

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Conclusions

• We studied a system of swarmalators that presents different phases.
• Analyzing the energy we noticed that near the transition to complete synchronization, it can be represented by an XY model which at first sight presentes a first order first transition.
• A closer analysis modifying the spectrum of natural frequencies show that the transition to synchronization shows a change of order.

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Thank you!