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Updated: Jul 16, 2025

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Synchronization onset for contrarians with higher-order interactions in multilayer systems.

Vasundhara Rathore1, Ayushi Suman2, Sarika Jalan1,2

  • 1Department of Biosciences and Biomedical Engineering, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, India.

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Introducing contrarians into multilayer networks with higher-order interactions can surprisingly aid synchronization. The multilayering strength controls this synchronization onset and phase transition, crucial for complex systems like the brain.

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Area of Science:

  • Complex systems
  • Network science
  • Nonlinear dynamics

Background:

  • Contrarians, individuals or elements with opposing views or behaviors, can significantly influence group dynamics.
  • Multilayer networks, representing systems with multiple interacting layers, offer a more realistic model for complex systems.
  • Higher-order interactions, beyond simple pairwise connections, are increasingly recognized in natural and social systems.

Purpose of the Study:

  • To investigate the effect of contrarian elements, modeled via negative coupling, on synchronization in multilayer networks with higher-order interactions.
  • To determine how multilayering strength and higher-order interactions influence the synchronization dynamics and phase transitions.

Main Methods:

  • Utilizing a multilayer network framework of phase oscillators.
  • Implementing negative coupling to represent contrarian influence.
  • Employing analytical calculations via the mean-field Ott-Antonsen approach.
  • Validating analytical findings through numerical simulations.

Main Results:

  • The multilayer framework facilitates synchronization onset even with negative pairwise coupling (contrarians).
  • Synchronization onset and the nature of the phase transition are governed by the multilayering strength.
  • Higher-order interactions determine the backward critical coupling.
  • A critical multilayering strength is necessary for the system to synchronize.

Conclusions:

  • Multilayer networks can promote synchronization in the presence of contrarian elements.
  • The interplay between multilayering strength and higher-order interactions is key to understanding synchronization in complex systems.
  • These findings offer insights into emergent behaviors in real-world systems like neural and social networks.