Synchronization and chimera states in time-varying multilayer networks with higher-order interactions

Most previous studies on eigenspectral analysis of synchronization have focused on static multilayer networks with pairwise interactions. In this work, we extend the analysis to time-varying multilayer networks with higher-order interactions. Specifically, we consider two types of multilayer connections, namely, multiplex and interconnected networks. For multiplex networks, we analytically derive the eigenspectra for an arbitrary number of layers with higher-order interactions. Our results show that stronger interlayer coupling accelerates the supra-diffusion process and suppresses multistable regions, while higher-order interactions further reduce the critical threshold required for the supra-diffusion process, fostering bistability and facilitating the emergence of chimera states. We numerically verify the results using a two-layer coupled pendulum network. For interconnected networks with time-varying interlayer interactions, we find that high-frequency switching between interlayer links disrupts interlayer synchronization, whereas low-frequency switching allows synchronization to emerge between layers. Under high switching frequency, increasing the switching probability has minimal influence on the synchronization patterns. Parameter-space analysis reveals the conditions under which interlayer synchronization and chimera states emerge or disappear, highlighting the interplay between interlayer and intralayer couplings. Analysis based on the master stability function confirms that synchronization becomes stable once the interlayer coupling surpasses a threshold.