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arXiv · 2508.06502

Enhancing cluster synchronization in phase-lagged multilayer networks

Abhijit Mondal·Pitambar Khanra·Subrata Ghosh·Prosenjit Kundu·Chittaranjan Hens·Pinaki Pal
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Abstract

Cluster synchronization in multilayer networks of phase oscillators with phase-lag poses significant challenges due to the destabilizing effects of delayed interactions. Leveraging the Sakaguchi-Kuramoto model, this study addresses these challenges by systematically exploring the role of natural frequency distributions in sustaining cluster synchronization under high phase-lag conditions. We focus on four distributions: uniform (uni-uni), partially degree-correlated (deg-uni, uni-deg), and fully degree-correlated (deg-deg), where oscillators' intrinsic frequencies align with their network connectivity. Through numerical and analytical investigations, we demonstrate that the deg-deg distribution, where both layers employ degree-matched frequencies, remarkably enhances synchronization stability, outperforming other configurations. We analyze two distinct network architectures: one composed entirely of nontrivial clusters and another combining trivial and nontrivial clusters. Results reveal that structural heterogeneity encoded in the deg-deg coupling counteracts phase-lag-induced desynchronization, enabling robust cluster synchronization even at large phase-lag values. Stability is rigorously validated via transverse Lyapunov exponents (TLEs), which confirm that deg-deg networks exhibit broader synchronization regimes compared to uniform or partially correlated systems. These findings provide critical insights into the interplay between topological heterogeneity and dynamical resilience, offering a framework for designing robust multilayer systems from delay-tolerant power grids to adaptive biological networks, where synchronization under phase-lag is paramount.

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Abhijit Mondal, Pitambar Khanra, Subrata Ghosh, Prosenjit Kundu, Chittaranjan Hens, Pinaki Pal. 2025-07-25. Enhancing cluster synchronization in phase-lagged multilayer networks. https://arxiv.org/abs/2508.06502

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