Generalized Master Stability of Heterogeneous Delay-Coupled Networks

Ana Elisa D. Barioni; Arthur N. Montanari; Adilson E. Motter

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arXiv · 2608.10076

Generalized Master Stability of Heterogeneous Delay-Coupled Networks

Ana Elisa D. Barioni·Arthur N. Montanari·Adilson E. Motter

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Abstract

Time delays are ubiquitous in physical and biological networked systems, playing a fundamental role in the emergence and stability of collective behavior. Yet, existing theoretical methods for synchronization analysis of delay-coupled systems are largely limited to networks with homogeneous degree distributions. Here, we extend the master stability function framework to a broad class of degree-heterogeneous, weighted, and directed delay-coupled networks. The analysis reveals that synchronization can be enhanced in heterogeneous networks compared to homogeneous ones, including all-to-all networks, which are known to be optimal in non-delayed systems. To identify optimal heterogeneous structures, we develop a network optimization method that finds directional, edge-weighted configurations maximizing synchronization stability. Our results show that, in delay-coupled networks, heterogeneity and nonreciprocity are key resources for synchronization.

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Ana Elisa D. Barioni, Arthur N. Montanari, Adilson E. Motter. 2026-08-10. Generalized Master Stability of Heterogeneous Delay-Coupled Networks. https://arxiv.org/abs/2608.10076

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