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Higher-order interactions induce stepwise explosive phase transitions.

Xueqi Li1, Palash Kumar Pal2, Youming Lei1,3

  • 1Northwestern Polytechnical University, School of Mathematics and Statistics, Xi'an 710072, China.

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Summary
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Researchers discovered a new stepwise explosive phase transition in coupled oscillators. This transition, driven by balanced interactions, offers new insights into network dynamics and desynchronization.

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Area of Science:

  • Physics
  • Complex Systems
  • Network Science

Background:

  • Coupled oscillators can exhibit continuous to explosive phase transitions.
  • Higher-order interactions play a crucial role in these transitions.

Purpose of the Study:

  • To identify and characterize a novel phase transition termed the stepwise explosive phase transition.
  • To investigate the role of competing interactions in coupled oscillator systems.

Main Methods:

  • Analysis of a globally frequency-weighted coupled pendulum model.
  • Construction of an analytical framework using self-consistent equations.

Main Results:

  • Identification of the stepwise explosive phase transition with multiple critical phase plateaus.
  • Demonstration that moderate higher-order attractive interactions and repulsive pairwise interactions trigger this transition.
  • Observation of partial frequency locking due to stronger higher-order interactions and weaker pairwise interactions.

Conclusions:

  • The stepwise explosive phase transition bridges continuous and explosive transitions.
  • This study reveals an alternative pathway to desynchronization in coupled networks.
  • Findings provide deeper insights into phase transitions within coupled dynamical networks.