Synchronization in Temporal Simplicial Complexes

Article Type

Research Article

Publication Title

SIAM Journal on Applied Dynamical Systems

Abstract

The stability analysis of synchronization in time-varying higher-order networked structures (simplicial complexes) is a challenging problem due to the presence of time-varying group interactions. In this context, most of the previous studies have been done either on temporal pairwise networks or on static simplicial complexes. Here, for the first time, we propose a general framework to study the synchronization phenomenon in temporal simplicial complexes. We show that the synchronous state exists as an invariant solution and obtain the necessary condition for it to emerge as a stable state in the fast-switching regime. We prove that the time-averaged simplicial complex plays the role of synchronization indicator whenever the switching among simplicial topologies is adequately fast. We attempt to transform the stability problem into a master stability function form. Unfortunately, for the general circumstances, the dimension reduction of the master stability equation is cumbersome due to the presence of group interactions. However, we overcome this difficulty in two interesting situations based on either the functional forms of the coupling schemes or the connectivity structure of the simplicial complex, and we demonstrate that the necessary condition mimics the form of a master stability function in these cases. We verify our analytical findings by applying them on synthetic and real-world networked systems. We find that the presence of temporality along with the multiway interactions improves the synchronization phenomena as compared to the static higher-ordered or temporal pairwise system. In addition, our results also reveal that with sufficient higher-order coupling and adequately fast rewiring, the temporal simplicial complex achieves synchrony even in a very low connectivity regime.

First Page

2054

Last Page

2081

DOI

https://10.1137/22M1525909

Publication Date

1-1-2023

Comments

Open Access, Green

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