Generalized adaptation-induced non-universal synchronization transitions in random hypergraphs

Area of Science:

• Complex systems
• Nonlinear dynamics
• Network science

Background:

• The Kuramoto model is a standard framework for studying synchronization in coupled oscillators.
• Understanding synchronization transitions in complex networks is crucial for various scientific fields.
• Hypergraph models offer a more general representation of interactions beyond pairwise connections.

Purpose of the Study:

• To investigate the impact of partial order parameter adaptation using general functions on oscillator synchronization.
• To explore synchronization behaviors in coupled Kuramoto oscillators on random hypergraphs with pairwise and triangular interactions.
• To analyze the emergence of diverse synchronization patterns under different adaptation strategies.

Main Methods:

• Utilizing the Ott-Antonsen ansatz to derive self-consistent equations for the order parameter.
• Modeling interactions between oscillators as pairwise and triangular within random hypergraph structures.
• Analyzing the effects of various generalized adaptation functions (e.g., power law, polynomial, Gaussian) on synchronization.

Main Results:

• Observed a wide range of synchronization transitions due to the interplay of adaptation, function type, and coupling strength.
• Identified a double-jump transition specifically under a power law adaptation function.
• Discovered the emergence of intermediate synchronization states with polynomial adaptation and specific coefficient combinations.
• Demonstrated that synchronization can be continuous or explosive based on pairwise coupling strength variations, also observed with Gaussian adaptation.

Conclusions:

• Partial order parameter adaptation in generalized forms significantly diversifies synchronization behaviors in coupled Kuramoto oscillators on hypergraphs.
• The choice of adaptation function critically influences the type and characteristics of observed synchronization transitions.
• The study highlights the rich dynamics and potential for complex synchronization phenomena in systems with higher-order interactions.