https://doi.org/10.1140/epjs/s11734-025-01789-4
Regular Article
Additive noise shapes the state and stability of random networks
1
MLMS, iCube, University of Strasbourg, 67000, Strasbourg, France
2
MIMESIS, INRIA Centre at University of Lorraine, 67000, Strasbourg, France
Received:
4
March
2025
Accepted:
6
July
2025
Published online:
21
July
2025
Natural systems are open to their environment and thus subjected to external perturbations. Some of such systems may be described as large randomly connected networks. The present work investigates how external additive random perturbations affect the state and stability of such finite-size random networks. We observe analytically an additive noise-induced system evolution (ANISE), whose stationary state depends on the additive noise level. In a first pilot study, the principal analytical approach is demonstrated by application to a nonlinear Erdos–Renyi network. In a second more detailed study, a nonlinear random network of excitatory and inhibitory sub-networks describes successfully Event-Related Desynchronization and Synchronization (ERD/ERS) observed in experimental brain signals. Here, we assume that underlying event-related processes tune the endogenous neural noise level. In sum, we find that additive noise impacts on the system’s stationary state and in turn also affects the system’s stability and hence its spectral properties.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
