Synchronization transitions in adaptive simplicial complexes with cooperative and competitive dynamics

TL;DR

This paper investigates how higher-order interactions and diverse adaptation types influence synchronization phase transitions in adaptive simplicial complexes, revealing transitions from first-order to second-order and the possibility of synchronization without pairwise interactions.

Contribution

It introduces a model incorporating higher-order interactions and cooperative/competitive adaptations, analyzing their effects on synchronization phase transitions.

Findings

Transition from first-order to second-order synchronization with increasing higher-order interaction strength.

Synchronization can occur without pairwise interactions if higher-order coupling is strong enough.

System exhibits different phase transition behaviors depending on adaptation types and coupling parameters.

Abstract

Adaptive network is a powerful presentation to describe different real-world phenomena. However, current models often neglect higher-order interactions (beyond pairwise interactions) and diverse adaptation types (cooperative and competitive) commonly observed in systems like the human brain and social networks. This work addresses this gap by incorporating these factors into a model that explores their impact on collective properties like synchronization. Through simplified network representations, we investigate how the simultaneous presence of cooperative and competitive adaptations influences phase transitions. Our findings reveal a transition from first-order to second-order synchronization as the strength of higher-order interactions increases under competitive adaptation. We also demonstrate the possibility of synchronization even without pairwise interactions, provided there is strong enough higher-order coupling. When only competitive adaptations are present, the system exhibits second-order-like phase transitions and clustering. Conversely, with a combination of cooperative and competitive adaptations, the system undergoes a first-order-like phase transition, characterized by a sharp transition to the synchronized state without reverting to an incoherent state during backward transitions. The specific nature of these second-order-like transitions varies depending on the coupling strengths and mean degrees. With our model, we can control not only when the system synchronizes but also the way the system goes to synchronization.