Contrarians Synchronize beyond the Limit of Pairwise Interactions

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Statistical Physics

Background:

• The Kuramoto model describes synchronization in populations of coupled oscillators.
• Traditional studies often focus on pairwise interactions.
• Understanding collective behavior in systems with higher-order interactions is crucial.

Purpose of the Study:

• To investigate the emergence of collective synchrony in Kuramoto oscillators with higher-order interactions.
• To explore the role of contrarian behavior and negative mean-field coupling.
• To provide an exact solution for the system's microscopic dynamics.

Main Methods:

• Analysis of globally coupled D-dimensional Kuramoto oscillators.
• Inclusion of higher-order interaction terms beyond pairwise coupling.
• Derivation of an exact solution for forward and backward transitions.

Main Results:

• Collective synchrony is achieved when interactions exceed pairwise limits.
• Higher-order interactions can induce coherence despite negative mean-field coupling.
• The system exhibits imperfect symmetry breaking into two phase-clustered states.

Conclusions:

• Group interactions, especially higher-order ones, are key to achieving synchrony in complex oscillator populations.
• This model provides insights into novel dynamical states and multidimensional choices in systems like social networks.
• The findings challenge traditional views limited to pairwise coupling dynamics.