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Robust observability and detectability of boolean networks under function perturbation

Fei Wang, Rong Zhao, Jun-e Feng and Biao Wang

International Journal of Systems Science, 2025, vol. 56, issue 10, 2311-2325

Abstract: This paper delves into the robust observability and robust (weak) detectability problems of Boolean networks (BNs) subject to function perturbation, which results in alterations to columns in the state transition matrix of BNs. To begin, based on whether transitions of states outside the set of perturbed points are affected, two distinct cases are introduced to analyze the evolution of state transitions at step k following the perturbation. Subsequently, the necessary and sufficient conditions for robust observability are established by examining changes of state transitions, employing a logical equation set. Additionally, a novel criterion to ascertain the (weak) detectability is proposed based on the data form of BNs, from which criteria are proposed to evaluate robust (weak) detectability. Finally, the main conclusions are illustrated with a numerical example and the p53-MDM2 negative feedback gene regulatory network.

Date: 2025
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DOI: 10.1080/00207721.2024.2447343

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