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Multibody interactions and nonlinear consensus dynamics on networked systems.

Leonie Neuhäuser1, Andrew Mellor2, Renaud Lambiotte2

  • 1Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom and Hertie School, Berlin 10117, Germany.

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Summary
This summary is machine-generated.

Multibody interactions on hypergraphs reveal complex dynamics beyond pairwise models. Nonlinearity is key for emergent effects, leading to state shifts and cluster dominance in consensus models.

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Area of Science:

  • Complex systems
  • Network science
  • Mathematical modeling

Background:

  • Traditional network models often use pairwise interactions, missing higher-order effects.
  • Consensus dynamics study how systems reach agreement, typically on networks.
  • Hypergraphs allow modeling of group interactions, going beyond pairwise connections.

Purpose of the Study:

  • To derive and analyze models for consensus dynamics on hypergraphs.
  • To investigate multibody dynamical effects beyond traditional two-body network models.
  • To explore how nonlinear interactions influence consensus and system states.

Main Methods:

  • Derivation and analysis of consensus dynamics models on hypergraphs.
  • Introduction of a nonlinear interaction function for three-body consensus.
  • Investigation of dynamics on modular hypergraphs with polarized clusters.

Main Results:

  • Multibody effects beyond pairwise interactions emerge only with nonlinear interaction functions.
  • Nonlinear consensus dynamics can lead to shifts away from the average system state.
  • Modular hypergraphs exhibit state-dependent, asymmetric dynamics, causing cluster dominance.

Conclusions:

  • Nonlinear interactions are crucial for observing higher-order dynamical effects in multibody systems.
  • Consensus dynamics on hypergraphs can exhibit complex behaviors like state shifts and polarization.
  • The interplay of initial states, structure, and interaction function dictates emergent dynamics.