Generalized Adaptation-Induced Non-universal Synchronization Transitions in Random Hypergraphs

TL;DR

This paper explores how partial, generalized adaptation functions influence synchronization transitions in coupled Kuramoto oscillators on random hypergraphs, revealing diverse behaviors including double-jump, intermediate, continuous, and explosive transitions.

Contribution

It introduces a generalized adaptation framework and demonstrates its impact on synchronization transitions, including novel phenomena like double-jump and intermediate states.

Findings

Double-jump transition under power-law adaptation

Emergence of intermediate states with polynomial adaptation

Transitions can be continuous or explosive depending on coupling strength

Abstract

We investigate the effect of partial order parameter adaptation in form of general functions on the synchronization behavior of coupled Kuramoto oscillators on top of random hypergraph models. The interactions between the oscillators are considered as pairwise and triangular. Using the Ott-Antonsen ansatz, we obtain a set of self-consistent equations of the order parameter that describe the synchronization diagrams. A broad diversity of synchronization transitions are observed as a result of the interaction between the partial adaptation approach, generalized adaptation functions, and coupling strengths. The system specifically shows a double-jump transition under a power-law form of the adaptation function. A polynomial form of the adaptation function leads to the emergence of an intermediate synchronization state for specific combinations of one negative and one positive coefficient. Moreover, the synchronization transition may become continuous or explosive when the pairwise coupling strength varies. The generality of this synchronization behavior is further supported by results obtained using a Gaussian adaptation function.