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D-dimensional oscillators in simplicial structures: Odd and even dimensions display different synchronization scenarios

Author

Listed:
  • Dai, X.
  • Kovalenko, K.
  • Molodyk, M.
  • Wang, Z.
  • Li, X.
  • Musatov, D.
  • Raigorodskii, A.M.
  • Alfaro-Bittner, K.
  • Cooper, G.D.
  • Bianconi, G.
  • Boccaletti, S.

Abstract

From biology to social science, the functioning of a wide range of systems is the result of elementary interactions which involve more than two constituents, so that their description has unavoidably to go beyond simple pairwise-relationships. Simplicial complexes are therefore the mathematical objects providing a faithful representation of such systems. We here present a complete theory of synchronization of D-dimensional oscillators obeying an extended Kuramoto model, and interacting by means of 1- and 2- simplices. Not only our theory fully describes and unveils the intimate reasons and mechanisms for what was observed so far with pairwise interactions, but it also offers predictions for a series of rich and novel behaviors in simplicial structures, which include: (a) a discontinuous de-synchronization transition at positive values of the coupling strength for all dimensions, (b) an extra discontinuous transition at zero coupling for all odd dimensions, and (c) the occurrence of partially synchronized states at D=2 (and all odd D) even for negative values of the coupling strength, a feature which is inherently prohibited with pairwise-interactions. Furthermore, our theory untangles several aspects of the emergent behavior: the system can never fully synchronize from disorder, and is characterized by an extreme multi-stability, in that the asymptotic stationary synchronized states depend always on the initial conditions. All our theoretical predictions are fully corroborated by extensive numerical simulations. Our results elucidate the dramatic and novel effects that higher-order interactions may induce in the collective dynamics of ensembles of coupled D-dimensional oscillators, and can therefore be of value and interest for the understanding of many phenomena observed in nature, like for instance the swarming and/or flocking processes unfolding in three or more dimensions.

Suggested Citation

  • Dai, X. & Kovalenko, K. & Molodyk, M. & Wang, Z. & Li, X. & Musatov, D. & Raigorodskii, A.M. & Alfaro-Bittner, K. & Cooper, G.D. & Bianconi, G. & Boccaletti, S., 2021. "D-dimensional oscillators in simplicial structures: Odd and even dimensions display different synchronization scenarios," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002411
    DOI: 10.1016/j.chaos.2021.110888
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    References listed on IDEAS

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    1. Jacopo Grilli & György Barabás & Matthew J. Michalska-Smith & Stefano Allesina, 2017. "Higher-order interactions stabilize dynamics in competitive network models," Nature, Nature, vol. 548(7666), pages 210-213, August.
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    3. Antoine Bricard & Jean-Baptiste Caussin & Nicolas Desreumaux & Olivier Dauchot & Denis Bartolo, 2013. "Emergence of macroscopic directed motion in populations of motile colloids," Nature, Nature, vol. 503(7474), pages 95-98, November.
    4. Iacopo Iacopini & Giovanni Petri & Alain Barrat & Vito Latora, 2019. "Simplicial models of social contagion," Nature Communications, Nature, vol. 10(1), pages 1-9, December.
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    1. Karimi Rahjerdi, Bahareh & Ramamoorthy, Ramesh & Nazarimehr, Fahimeh & Rajagopal, Karthikeyan & Jafari, Sajad, 2022. "Indicating the synchronization bifurcation points using the early warning signals in two case studies: Continuous and explosive synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Tadić, Bosiljka & Chutani, Malayaja & Gupte, Neelima, 2022. "Multiscale fractality in partial phase synchronisation on simplicial complexes around brain hubs," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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