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Multistability in coupled oscillator systems with higher-order interactions and community structure.

Per Sebastian Skardal1, Sabina Adhikari2, Juan G Restrepo2

  • 1Department of Mathematics, Trinity College, Hartford, Connecticut 06106, USA.

Chaos (Woodbury, N.Y.)
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Summary
This summary is machine-generated.

We investigated coupled phase oscillators with higher-order interactions and community structure. This revealed novel synchronized states and multistability, offering new insights into complex system dynamics.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Network Science

Background:

  • Coupled oscillator systems are fundamental to understanding emergent phenomena.
  • Previous studies often focused on pairwise interactions or simple network structures.
  • The interplay of higher-order interactions and community structure in oscillator synchronization remains underexplored.

Purpose of the Study:

  • To investigate the synchronization dynamics of coupled phase oscillators incorporating both higher-order interactions and community structure.
  • To identify novel synchronized states and emergent behaviors arising from the combination of these features.
  • To analyze the stability and coexistence of these states within the system.

Main Methods:

  • Derivation of low-dimensional dynamics for the coupled oscillator system.
  • Employing stability analysis to determine the conditions for stable states.
  • Utilizing perturbation theory to examine system bifurcations.
  • Numerical simulations to validate analytical findings.

Main Results:

  • The combination of higher-order interactions and community structure supports unique synchronized states not observed in simpler models.
  • Identified synchronized states include in-phase, anti-phase, and a novel skew-phase clustering within communities.
  • Observed an incoherent-synchronized state, indicating partial order within the population.
  • Demonstrated strong multistability, with multiple distinct synchronized states coexisting stably.

Conclusions:

  • Higher-order interactions and community structure synergistically create complex synchronization patterns in oscillator populations.
  • The identified novel states and multistability highlight the richness of dynamics in structured complex systems.
  • This work provides a theoretical framework for understanding synchronization in networks with intricate interaction topologies.