Stability analysis of intralayer synchronization in time-varying multilayer networks with generic coupling functions

TL;DR

This paper analyzes the stability of intralayer synchronization in time-varying multilayer hypernetworks with generic coupling functions, providing conditions for stable synchronization using analytical and numerical methods.

Contribution

It introduces a novel stability analysis framework for intralayer synchronization in dynamic multilayer hypernetworks with arbitrary coupling functions.

Findings

Derived stability conditions using time-averaged network structures.

Separated transverse subspace for stability analysis.

Validated results through numerical simulations on neuronal networks.

Abstract

The stability analysis of synchronization patterns on generalized network structures is of immense importance nowadays. In this article, we scrutinize the stability of intralayer synchronous state in temporal multilayer hypernetworks, where each dynamic units in a layer communicate with others through various independent time-varying connection mechanisms. Here, dynamical units within and between layers may be interconnected through arbitrary generic coupling functions. We show that intralayer synchronous state exists as an invariant solution. Using fast switching stability criteria, we derive the condition for stable coherent state in terms of associated time-averaged network structure, and in some instances we are able to separate the transverse subspace optimally. Using simultaneous block diagonalization of coupling matrices, we derive the synchronization stability condition without considering time-averaged network structure. Finally, we verify our analytically derived results through a series of numerical simulations on synthetic and real-world neuronal networked systems.