Stability of synchronization in simplicial complexes with multiple interaction layers
Abstract
Understanding how the interplay between higher-order and multilayer structures of interconnections influences the synchronization behaviors of dynamical systems is a feasible problem of interest, with possible application in essential topics such as neuronal dynamics. Here, we provide a comprehensive approach for analyzing the stability of the complete synchronization state in simplicial complexes with numerous interaction layers. We show that the synchronization state exists as an invariant solution and derive the necessary condition for a stable synchronization state in presence of general coupling functions. It generalizes the well-known master stability function scheme to the higher-order structures with multiple interaction layers. We verify our theoretical results by employing them on networks of paradigmatic R\"{o}ssler oscillators and Sherman neuronal models, and demonstrate that the presence of group interactions considerably improves the synchronization phenomenon in the multilayer framework.
Cite
@article{arxiv.2209.00825,
title = {Stability of synchronization in simplicial complexes with multiple interaction layers},
author = {Md Sayeed Anwar and Dibakar Ghosh},
journal= {arXiv preprint arXiv:2209.00825},
year = {2022}
}
Comments
14 pages, 5 figures; Accepted for publication in Physical Review E (2022)