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arXiv · 2610.17150

Global synchronization in time-varying directed higher-order networks

Wilfried Segnou·Timoteo Carletti·Dibakar Ghosh
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Abstract

Global synchronization has been largely investigated in static higher-order networks and little attention has been brought to directed, temporal higher-order networks. We hereby make a step in this direction by studying the emergence of global synchronization in periodically fast switching systems with directed higher-order interactions. By working in the framework of the Master Stability Function, we show that the linearized dynamics includes two time-dependent Jacobian matrices, both evolving on the timescale of the synchronous solution, together with a generalized Laplacian evolving on a fast switching timescale, resulting from the hypergraph time evolution. To address this two-timescale structure, we establish a fast-switching stability criterion for directed balanced higher-order structures. The latter condition allows to decouple the parallel and transverse perturbations to the synchronization manifold. By relying on the average theory for dynamical systems, we are able to prove exponential stability of global synchronization in the fast switching higher-order network. The proposed theory is then illustrated by using a higher-order Stuart--Landau model, which provides a natural benchmark for the theory. Directionality can move Laplacian eigenvalues into instability regions off the real axis, hence destabilizing synchronization; our results nevertheless reveal that temporal switching can counteract this destabilizing effect and restore global synchronization when the directed structures alternate sufficiently rapidly, even though the instantaneous directed higher-order structures are individually unstable.

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Wilfried Segnou, Timoteo Carletti, Dibakar Ghosh. 2026-10-12. Global synchronization in time-varying directed higher-order networks. https://arxiv.org/abs/2610.17150

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