Global synchronization of topological signals with time-delayed interactions
Abstract
Topological signals are dynamical variables supported on higher-order structures such as simplicial or cell complexes. In this work, we investigate the impact of time-delayed interactions on the emergence of global synchronization of topological oscillators, with application to the Stuart-Landau system. We first examine the case where signals are supported on simplexes, or cells, of a given dimension and coupled through the Hodge-Laplace matrix. We derive the Master Stability Function and we prove that for suitable discrete delay values, the stability of the synchronous solution becomes analytically tractable and can be solved by using the Lambert W-function. This analysis yields explicit spectral conditions for Global Topological Synchronization to emerge and shows that admissible delays may either promote or suppress synchronization. We then study delayed interactions between signals supported on simplexes, or cells, of different dimensions coupled by the Dirac operator. Under analogous admissible time delays the variational problem, still related to the Master Stability Function, can again be simplified, however in this case we prove that Global Topological Dirac Synchronization cannot emerge. Numerical simulations on simplicial and cell complexes corroborate and complement these findings.
Related
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BibTeX
@misc{segnou2026global,
title = {{Global synchronization of topological signals with time-delayed interactions}},
author = {Wilfried Segnou and Thierry Njougouo and Diego Garlaschelli and Timoteo Carletti},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34609},
eprint = {2609.34609},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34609},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Global synchronization of topological signals with time-delayed interactions
AU - Wilfried Segnou
AU - Thierry Njougouo
AU - Diego Garlaschelli
AU - Timoteo Carletti
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34609
UR - https://arxiv.org/abs/2609.34609
AB - Topological signals are dynamical variables supported on higher-order structures such as simplicial or cell complexes. In this work, we investigate the impact of time-delayed interactions on the emergence of global synchronization of topological oscillators, with application to the Stuart-Landau system. We first examine the case where signals are supported on simplexes, or cells, of a given dimension and coupled through the Hodge-Laplace matrix. We derive the Master Stability Function and we prove that for suitable discrete delay values, the stability of the synchronous solution becomes analytically tractable and can be solved by using the Lambert W-function. This analysis yields explicit spectral conditions for Global Topological Synchronization to emerge and shows that admissible delays may either promote or suppress synchronization. We then study delayed interactions between signals supported on simplexes, or cells, of different dimensions coupled by the Dirac operator. Under analogous admissible time delays the variational problem, still related to the Master Stability Function, can again be simplified, however in this case we prove that Global Topological Dirac Synchronization cannot emerge. Numerical simulations on simplicial and cell complexes corroborate and complement these findings.
ER -